Question ID stringlengths 4 4 | Model Name stringclasses 3
values | Topic stringclasses 10
values | Difficulty stringclasses 3
values | Question stringlengths 16 187 | Correct Answer stringlengths 2 44 | Verified Solution stringlengths 2 44 | AI Response stringlengths 166 4.88k | Correctness Score float64 5 5 ⌀ | Reasoning Score float64 3 5 ⌀ | Clarity Score float64 3 5 ⌀ | Error Type stringclasses 1
value | Final Score int64 0 100 | Evaluator Explanation stringlengths 17 160 ⌀ |
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M001 | GPT-4o | Percentages | Easy | A shirt marked at ₹2,000 is sold at a discount of 15%. Find its selling price. | Selling Price is ₹1,700 | Selling Price is ₹1,700 | Step 1: Identify the marked price.
Marked Price = ₹2,000
Step 2: Calculate the discount.
Discount = 15% of ₹2,000
= (15/100) × 2,000
= ₹300
Step 3: Calculate the selling price.
Selling Price = Marked Price − Discount
= ₹2,000 − ₹300
= ₹1,700
Final Answer: ₹1,700 | 5 | 4 | 4 | No Error | 90 | Given values are not mentioned at starting, Mentioning given information is important before starting maths |
M001 | Claude | Percentages | Easy | A shirt marked at ₹2,000 is sold at a discount of 15%. Find its selling price. | Selling Price is ₹1,700 | Selling Price is ₹1,700 | Solution
Given:
- Marked Price (MP) = Rs. 2,000
- Discount = 15%
Step 1: Calculate the Discount Amount
Discount Amount = (Discount % / 100) x Marked Price
= (15 / 100) x 2000
= 30000 / 100
= Rs. 300
Step 2: Calculate the Selling Price
Selling Price = Marked Price - Discou... | 5 | 4 | 5 | No Error | 94 | All Correct, all Steps are Clearly shown. |
M001 | Gemini | Percentages | Easy | A shirt marked at ₹2,000 is sold at a discount of 15%. Find its selling price. | Selling Price is ₹1,700 | Selling Price is ₹1,700 | Here is the step by step solution:
Given information:
Marked price of the shirt = 2000 rupees
Discount rate = 15 percent
Step 1: Calculate the discount amount.
The discount amount is 15 percent of the marked price.
Discount = (15 / 100) x 2000
Discount = 0.15 x 2000
Discount = 300 rupees
Step 2: Calculate the sellin... | 5 | 4 | 4 | No Error | 90 | Rupees symbol is missing, im mathematics symbols are more prominent to use everytime otherthan words. |
M002 | GPT-4o | Percentages | Medium | A number is increased by 20% and then decreased by 20%. What is the overall percentage change? | 4% Reduced | 4% Reduced | Let the original number be 100.
Step 1: Increase the number by 20%.
20% of 100 = 20
New number = 100 + 20 = 120
Step 2: Decrease the new number by 20%.
20% of 120 = 24
New number = 120 − 24 = 96
Step 3: Compare the final number with the original number.
Original number = 100
Final number = 96
Decrease = 100 − 96 = 4... | 5 | 4 | 4 | No Error | 90 | Why 100 is taken is not explained properly, important to mention that - 100 is easy to calculate. Calculation steps are missing |
M002 | Claude | Percentages | Medium | A number is increased by 20% and then decreased by 20%. What is the overall percentage change? | 4% Reduced | 4% Reduced | Solution
Given:
- A number is first increased by 20%, then decreased by 20%.
- Find the overall percentage change.
Step 1: Assume a convenient starting number
Let the original number = 100
(We use 100 to make percentage calculations easy.)
Step 2: Increase the number by 20%
Increase Amount = 20% of 100
... | 5 | 5 | 4 | No Error | 96 | Well structured and all steps clearl shown, but not mentioned increasing means addition and decreasing means subtraction |
M002 | Gemini | Percentages | Medium | A number is increased by 20% and then decreased by 20%. What is the overall percentage change? | 4% Reduced | 4% Reduced | Let the initial number be 100 to make the calculations clear.
Step 1: Calculate the value after the 20% increase.
A 20% increase means adding 20% of the original number to itself.
20% of 100 = (20 / 100) x 100 = 20
Increased number = 100 + 20 = 120
Step 2: Calculate the value after the 20% decrease.
The new starting ... | 5 | 5 | 5 | No Error | 100 | All steps are clearly shown |
M003 | GPT-4o | Percentages | Medium | The price of a book increases from ₹400 to ₹460. Find the percentage increase. | 15% increased | 15% increased | Step 1: Identify the original price.
Original price = ₹400
Step 2: Find the increase in price.
Increase = New price − Original price
= ₹460 − ₹400
= ₹60
Step 3: Calculate the percentage increase.
Percentage increase = (Increase / Original price) × 100
= (60 / 400) × 100
= 15%
Final Answer: 15% increase. | 5 | 4 | 4 | No Error | 90 | All the given values are not mentioned at starting, Why comparing with Original price is not explanied. |
M003 | Claude | Percentages | Medium | The price of a book increases from ₹400 to ₹460. Find the percentage increase. | 15% increased | 15% increased | Solution
Given:
- Original Price = Rs. 400
- New Price = Rs. 460
- Find the percentage increase
Step 1: Find the Amount of Increase
Increase = New Price - Original Price
= Rs. 460 - Rs. 400
= Rs. 60
Step 2: Apply the Percentage Increase Formula
Percentage Increase = (Increase / Original Price) x 1... | 5 | 4 | 5 | No Error | 94 | All steps are organized properly, key points are helpful |
M003 | Gemini | Percentages | Medium | The price of a book increases from ₹400 to ₹460. Find the percentage increase. | 15% increased | 15% increased | Here is the step by step solution:
Given information:
Initial price of the book = 400 rupees
Final price of the book = 460 rupees
Step 1: Calculate the increase in price.
The increase in price is the difference between the final price and the initial price.
Increase = Final price - Initial price
Increase = 460 - 400
... | 5 | 4 | 4 | No Error | 90 | Why comparing with intial price is not explained properly |
M004 | GPT-4o | Percentages | Hard | A person's salary is increased by 25% and then decreased by 20%. If the original salary was ₹40,000, what is the final salary and what is the overall percentage change? | Final Salary is 40,000, 0% change | Final Salary is 40,000, 0% change | Step 1: Identify the original salary.
Original salary = ₹40,000
Step 2: Increase the salary by 25%.
Increase = 25% of ₹40,000
= (25/100) × 40,000
= ₹10,000
New salary = ₹40,000 + ₹10,000
= ₹50,000
Step 3: Decrease the new salary by 20%.
Decrease = 20% of ₹50,000
= (20/100) × 50,000
= ₹10,000
Final salary = ₹50,000 −... | 5 | 5 | 4 | No Error | 96 | Even though the chages are different 20% and 25%, why the final amount aslo same as original one is not explained |
M004 | Claude | Percentages | Hard | A person's salary is increased by 25% and then decreased by 20%. If the original salary was ₹40,000, what is the final salary and what is the overall percentage change? | Final Salary is 40,000, 0% change | Final Salary is 40,000, 0% change | Solution
Given:
- Original Salary = Rs. 40,000
- First Change: Increase by 25%
- Second Change: Decrease by 20%
- Find the final salary and overall percentage change.
Step 1: Increase the salary by 25%
Increase Amount = 25% of Rs. 40,000
= (25 / 100) x 40,000
= Rs. 10,000
Salary after in... | 5 | 5 | 5 | No Error | 100 | All steps are explained correctly |
M004 | Gemini | Percentages | Hard | A person's salary is increased by 25% and then decreased by 20%. If the original salary was ₹40,000, what is the final salary and what is the overall percentage change? | Final Salary is 40,000, 0% change | Final Salary is 40,000, 0% change | Here is the step by step solution:
Given information:
Original salary = 40000 rupees
First change = 25 percent increase
Second change = 20 percent decrease
Step 1: Calculate the salary after the 25 percent increase.
The increase amount is 25 percent of the original salary.
Increase = (25 / 100) x 40000
Increase = 0.2... | 5 | 4 | 4 | No Error | 90 | Usage of Precentage symbole is missing and Why original and final salary is same even though the changes is different is not explaiend |
M005 | GPT-4o | Percentages | Hard | In an examination, a student scores 30% and fails by 12 marks. Another student scores 42% and gets 24 marks more than the passing marks. Find the maximum marks and the passing percentage. | Maximum marks is 300, pass percentage is 34% | Maximum marks is 300, pass percenrage is 34% | Let the maximum marks be M and the passing marks be P.
Step 1: Use the first student's information.
First student scores 30% and fails by 12 marks.
So, passing marks = 30% of M + 12
P = 30% of M + 12
Step 2: Use the second student's information.
Second student scores 42% and gets 24 marks more than the passing marks.... | 5 | 4 | 5 | No Error | 94 | In step 1 why 12 is adding and in step 2 why 24 is substracting is not explained |
M005 | Claude | Percentages | Hard | In an examination, a student scores 30% and fails by 12 marks. Another student scores 42% and gets 24 marks more than the passing marks. Find the maximum marks and the passing percentage. | Maximum marks is 300, pass percentage is 34% | Maximum marks is 300, pass percenrage is 34% | Solution
Given:
- Student 1 scores 30% and fails by 12 marks.
- Student 2 scores 42% and scores 24 marks more than the passing marks.
- Find the maximum marks and the passing percentage.
Step 1: Set up variables
Let Maximum Marks = M
Let Passing Marks = P
Step 2: Form two equations
Student 1 scores 30% but falls SH... | 5 | 5 | 3 | No Error | 92 | Final answer is correct but the calaculation is tough to understand, calrity is missing in calculation. |
M005 | Gemini | Percentages | Hard | In an examination, a student scores 30% and fails by 12 marks. Another student scores 42% and gets 24 marks more than the passing marks. Find the maximum marks and the passing percentage. | Maximum marks is 300, pass percentage is 34% | Maximum marks is 300, pass percenrage is 34% | Here is the step by step solution:
Let the maximum marks be x and the passing marks be P.
Step 1: Write down the equations based on the given information.
For the first student:
The score is 30 percent of the maximum marks, which is 12 marks less than the passing marks.
0.30x = P - 12
Therefore, P = 0.30x + 12 (Equati... | 5 | 4 | 4 | No Error | 90 | Converting percantages into deciaml points in step1 and step2 is not neccesary it will creates calculation misunderstanding. |
M006 | GPT-4o | Ratio & Proportion | Easy | The ratio of boys to girls in a class is 3:2. If there are 25 students in the class, how many are boys? | 15 boys | 15 boys | Step 1: Identify the ratio.
Boys : Girls = 3 : 2
Total parts = 3 + 2 = 5 parts
Step 2: Find the value of one part.
Total students = 25
One part = 25 ÷ 5 = 5 students
Step 3: Find the number of boys.
Boys = 3 parts
= 3 × 5
= 15 students
Final Answer: 15 boys. | 5 | 4 | 3 | No Error | 86 | Not explained what is the mean of Ratio, missing clarity |
M006 | Claude | Ratio & Proportion | Easy | The ratio of boys to girls in a class is 3:2. If there are 25 students in the class, how many are boys? | 15 boys | 15 boys | Given:
- Ratio of Boys to Girls = 3 : 2
- Total number of students = 25
- Find the number of boys.
Step 1: Understand what the ratio means
Boys : Girls = 3 : 2
This means for every 3 boys, there are 2 girls.
In other words, out of every 5 students, 3 are boys and 2 are girls.
Total number of parts = 3 + 2 = 5 parts
... | 5 | 4 | 4 | No Error | 90 | Correct explantion of core concept called Ratio, but why adding 2 and 3 in step1 is not exlpained |
M006 | Gemini | Ratio & Proportion | Easy | The ratio of boys to girls in a class is 3:2. If there are 25 students in the class, how many are boys? | 15 boys | 15 boys | Given information:
Ratio of boys to girls = 3:2
Total number of students = 25
Step 1: Calculate the total number of parts in the ratio.
The ratio of boys to girls is 3:2, which means there are 3 parts for boys and 2 parts for girls.
Total parts = 3 + 2 = 5
Step 2: Calculate the value of one part.
Divide the total num... | 5 | 4 | 4 | No Error | 90 | Not explained what is the mean of Ratio, and Total parts concept |
M007 | GPT-4o | Ratio & Proportion | Easy | ₹720 is divided between A and B in the ratio 5:7. Find B's share. | B's share is ₹420 | B's share is ₹420 | Step 1: Identify the ratio.
A : B = 5 : 7
Total parts = 5 + 7 = 12 parts
Step 2: Find the value of one part.
Total amount = ₹720
One part = ₹720 ÷ 12
= ₹60
Step 3: Find B's share.
B has 7 parts.
B's share = 7 × ₹60
= ₹420
Final Answer: B's share = ₹420. | 5 | 4 | 3 | No Error | 86 | Not explained what is the mean of Ratio, missing clarity |
M007 | Claude | Ratio & Proportion | Easy | ₹720 is divided between A and B in the ratio 5:7. Find B's share. | B's share is ₹420 | B's share is ₹420 | Given:
- Total amount = Rs. 720
- Ratio of A : B = 5 : 7
- Find B's share.
Step 1: Understand what the ratio means
A : B = 5 : 7
This means for every Rs. 5 that A receives,
B receives Rs. 7.
Total number of parts = 5 + 7 = 12 parts
Step 2: Find the value of one part
Total amount = Rs. 720
One part = Total amount / To... | 5 | 4 | 4 | No Error | 90 | Correct explantion of core concept called Ratio, but why adding 5 and 7 in step1 is not exlpained |
M007 | Gemini | Ratio & Proportion | Easy | ₹720 is divided between A and B in the ratio 5:7. Find B's share. | B's share is ₹420 | B's share is ₹420 | Given information:
Total amount to be divided = 720 rupees
Ratio of A's share to B's share = 5:7
Step 1: Calculate the total number of parts in the ratio.
The ratio is 5:7, meaning A gets 5 parts and B gets 7 parts.
Total parts = 5 + 7 = 12
Step 2: Calculate the value of one part.
Divide the total amount by the total... | 5 | 4 | 4 | No Error | 90 | Not explained what is the mean of Ratio, and Total parts concept |
M008 | GPT-4o | Ratio & Proportion | Medium | The ratio of the present ages of A and B is 4:5. After 6 years, their ages will be in the ratio 5:6. Find their present ages. | Present ages of A and B are 24 and 30 years | Present ages of A and B are 24 and 30 years | Let the present ages of A and B be 4x and 5x.
Step 1: Write their ages after 6 years.
A's age after 6 years = 4x + 6
B's age after 6 years = 5x + 6
Their ratio after 6 years is 5:6.
Therefore,
(4x + 6) : (5x + 6) = 5 : 6
Step 2: Cross-multiply.
6(4x + 6) = 5(5x + 6)
24x + 36 = 25x + 30
Step 3: Solve for x.
25x − 24x... | 5 | 4 | 5 | No Error | 94 | Considering x is not explained at the staring of the solution, step2 also not clearly explaiend about why cross multiplication. |
M008 | Claude | Ratio & Proportion | Medium | The ratio of the present ages of A and B is 4:5. After 6 years, their ages will be in the ratio 5:6. Find their present ages. | Present ages of A and B are 24 and 30 years | Present ages of A and B are 24 and 30 years | Given:
- Present ratio of ages of A and B = 4 : 5
- After 6 years, ratio of their ages = 5 : 6
- Find their present ages.
Step 1: Assign variables using the given ratio
Let the common multiplier = x
Present age of A = 4x
Present age of B = 5x
Step 2: Set up ages after 6 years
After 6 years:
Age of A = 4x + 6
Age of ... | 5 | 4 | 5 | No Error | 94 | Converting Ratio into division in step 3 is not expalined properly |
M008 | Gemini | Ratio & Proportion | Medium | The ratio of the present ages of A and B is 4:5. After 6 years, their ages will be in the ratio 5:6. Find their present ages. | Present ages of A and B are 24 and 30 years | Present ages of A and B are 24 and 30 years | Given information:
The ratio of the present ages of A and B is 4:5.
The ratio of their ages after 6 years will be 5:6.
Step 1: Set up the variables for their present ages.
Since the ratio of their present ages is 4:5, let a common multiplier be x.
Present age of A = 4x
Present age of B = 5x
Step 2: Express their ages... | 5 | 5 | 5 | No Error | 100 | Converting Ratio into division in step 3 is not expalined properly |
M009 | GPT-4o | Ratio & Proportion | Medium | If a:b = 3:4 and b:c = 8:9, find a:b:c. | 6:8:9 | 6:8:9 | Step 1: Write the given ratios.
a : b = 3 : 4
b : c = 8 : 9
Step 2: Make the value of b the same in both ratios.
In the first ratio:
a : b = 3 : 4
Multiply both terms by 2:
a : b = 6 : 8
The second ratio is:
b : c = 8 : 9
Step 3: Combine the ratios.
a : b = 6 : 8
b : c = 8 : 9
Therefore,
a : b : c = 6 : 8 : 9
Fina... | 5 | 5 | 4 | No Error | 96 | Why making b value is same is not explained |
M009 | Claude | Ratio & Proportion | Medium | If a:b = 3:4 and b:c = 8:9, find a:b:c. | 6:8:9 | 6:8:9 | Given:
- a : b = 3 : 4
- b : c = 8 : 9
- Find a : b : c
Step 1: Understand the requirement
To combine two separate ratios into one combined ratio,
the value of the COMMON term (b) must be the SAME in
both ratios. Currently b = 4 in the first ratio and
b = 8 in the second ratio. We need to make them equal.
Step 2: Fin... | 5 | 5 | 4 | No Error | 96 | Very step is clearly explained, but why LCM only is not explaiend. |
M009 | Gemini | Ratio & Proportion | Medium | If a:b = 3:4 and b:c = 8:9, find a:b:c. | 6:8:9 | 6:8:9 | Given information:
The ratio a:b = 3:4
The ratio b:c = 8:9
Step 1: Identify the common term in both ratios.
The common term in both ratios is b. In the first ratio (a:b = 3:4), the value corresponding to b is 4. In the second ratio (b:c = 8:9), the value corresponding to b is 8.
Step 2: Make the common term equal in ... | 5 | 5 | 4 | No Error | 96 | Very step is clearly explained, but why LCM only is not explaiend. |
M010 | GPT-4o | Ratio & Proportion | Hard | A sum of money is divided among A, B and C in the ratio 2:3:5. If C receives ₹1,200 more than A, find the total amount distributed. | ₹4,000 | ₹4,000 | Step 1: Identify the ratio.
A : B : C = 2 : 3 : 5
Step 2: Find the difference between C's share and A's share.
C − A = 5 parts − 2 parts
= 3 parts
We are given that C receives ₹1,200 more than A.
So, 3 parts = ₹1,200
Step 3: Find the value of one part.
1 part = ₹1,200 ÷ 3
= ₹400
Step 4: Find the total number of par... | 5 | 3 | 3 | No Error | 80 | The core concept of Ratio and considering parts is not explained, not clarity and proper reasoning. |
M010 | Claude | Ratio & Proportion | Hard | A sum of money is divided among A, B and C in the ratio 2:3:5. If C receives ₹1,200 more than A, find the total amount distributed. | ₹4,000 | ₹4,000 | Given:
- Ratio of A : B : C = 2 : 3 : 5
- C receives Rs. 1,200 more than A
- Find the total amount distributed.
Step 1: Assign variables using the given ratio
Let the common multiplier = x
A's share = 2x
B's share = 3x
C's share = 5x
Step 2: Form an equation using the given condition
C receives Rs. 1,200 more than A,... | 5 | 5 | 4 | No Error | 96 | Ratio concpet is not explained. |
M010 | Gemini | Ratio & Proportion | Hard | A sum of money is divided among A, B and C in the ratio 2:3:5. If C receives ₹1,200 more than A, find the total amount distributed. | ₹4,000 | ₹4,000 | Given information:
The sum of money is divided among A, B, and C in the ratio 2:3:5.
C receives 1200 rupees more than A.
Step 1: Set up the variables based on the ratio.
Let the common multiplier be x.
A's share = 2x
B's share = 3x
C's share = 5x
Step 2: Set up the equation based on the given condition.
We know that ... | 5 | 5 | 4 | No Error | 96 | Ratio concpet and considering parts is not explained. |
M011 | GPT-4o | Avarage | Easy | The average of five numbers is 24. Four of the numbers are 18, 21, 27 and 30. Find the fifth number. | Fifth number is 24 | Fifth number is 24 | Step 1: Find the total of all five numbers.
Average = 24
Number of numbers = 5
Total = Average × Number of numbers
= 24 × 5
= 120
Step 2: Add the four known numbers.
18 + 21 + 27 + 30 = 96
Step 3: Find the fifth number.
Fifth number = Total − Sum of four numbers
= 120 − 96
= 24
Final Answer: 24 | 5 | 4 | 4 | No Error | 90 | Narrow answer, no concept is explained. |
M011 | Claude | Avarage | Easy | The average of five numbers is 24. Four of the numbers are 18, 21, 27 and 30. Find the fifth number. | Fifth number is 24 | Fifth number is 24 | Given:
- Average of five numbers = 24
- Four known numbers = 18, 21, 27 and 30
- Find the fifth number.
Step 1: Recall the average formula
Average = Sum of all numbers / Count of numbers
Rearranging to find the total sum:
Total Sum = Average x Count of numbers
Step 2: Find the total sum of all five numbers
Total Sum ... | 5 | 5 | 5 | No Error | 100 | Core concept is explained correclty, all steps are well organied. |
M011 | Gemini | Avarage | Easy | The average of five numbers is 24. Four of the numbers are 18, 21, 27 and 30. Find the fifth number. | Fifth number is 24 | Fifth number is 24 | Given information:
Average of five numbers = 24
Four of the numbers = 18, 21, 27, 30
Step 1: Calculate the total sum of the five numbers.
The total sum is the average multiplied by the number of values.
Total sum = 24 x 5
Total sum = 120
Step 2: Calculate the sum of the four known numbers.
Sum of given numbers = 18 +... | 5 | 4 | 4 | No Error | 90 | Core concept is missing in explanation |
M012 | GPT-4o | Avarage | Easy | The average age of 10 students is 15 years. If a teacher aged 35 years joins them, what is the new average age? | 16.8181..... (or) 16 9/11 | 16.8181..... (or) 16 9/11 | Step 1: Find the total age of the 10 students.
Average age = 15 years
Number of students = 10
Total age = 15 × 10
= 150 years
Step 2: Add the teacher's age.
Teacher's age = 35 years
New total age = 150 + 35
= 185 years
Step 3: Find the new number of people.
10 students + 1 teacher = 11 people
Step 4: Calculate the n... | 5 | 5 | 4 | No Error | 96 | Average concept is not explained properly, missing clarity. |
M012 | Claude | Avarage | Easy | The average age of 10 students is 15 years. If a teacher aged 35 years joins them, what is the new average age? | 16.8181..... (or) 16 9/11 | 16.8181..... (or) 16 9/11 | Given:
- Average age of 10 students = 15 years
- Age of teacher = 35 years
- Find the new average age when the teacher joins the group.
Step 1: Find the total age of the 10 students
Total Age = Average x Count of students
= 15 x 10
= 150 years
Step 2: Find the new total age after teacher joins
New... | 5 | 4 | 5 | No Error | 94 | Missing Avegare Fromula, missing reasoning in step1 |
M012 | Gemini | Avarage | Easy | The average age of 10 students is 15 years. If a teacher aged 35 years joins them, what is the new average age? | 16.8181..... (or) 16 9/11 | 16.8181..... (or) 16 9/11 | Given information:
Number of students = 10
Average age of students = 15 years
Age of the teacher = 35 years
Step 1: Calculate the total age of the 10 students.
The total age is the average age multiplied by the number of students.
Total age of students = 10 x 15
Total age of students = 150 years
Step 2: Calculate the... | 5 | 5 | 4 | No Error | 96 | Average concept is not explained properly |
M013 | GPT-4o | Avarage | Medium | The average marks of 20 students is 64. If the average marks of 12 students is 70, find the average marks of the remaining 8 students. | 8 students avarage marks is 55 | 8 students avarage marks is 55 | Step 1: Find the total marks of all 20 students.
Average marks = 64
Number of students = 20
Total marks = 64 × 20
= 1280 marks
Step 2: Find the total marks of the 12 students.
Average marks = 70
Number of students = 12
Total marks = 70 × 12
= 840 marks
Step 3: Find the total marks of the remaining 8 students.
Total m... | 5 | 4 | 4 | No Error | 90 | Average concept is not explained properly, missing clarity. |
M013 | Claude | Avarage | Medium | The average marks of 20 students is 64. If the average marks of 12 students is 70, find the average marks of the remaining 8 students. | 8 students avarage marks is 55 | 8 students avarage marks is 55 | Given:
- Average marks of all 20 students = 64
- Number of students in first group = 12, their average = 70
- Number of students in second group = 8
- Find the average marks of the remaining 8 students.
Step 1: Find the total marks of all 20 students
Total Marks = Average x Count
= 64 x 20
= 1,... | 5 | 4 | 4 | No Error | 90 | Missing the clarity in Average concept. |
M013 | Gemini | Avarage | Medium | The average marks of 20 students is 64. If the average marks of 12 students is 70, find the average marks of the remaining 8 students. | 8 students avarage marks is 55 | 8 students avarage marks is 55 | Given information:
Total number of students = 20
Average marks of all 20 students = 64
Number of students in the first group = 12
Average marks of these 12 students = 70
Number of remaining students = 8
Step 1: Calculate the total marks of all 20 students.
The total marks for the whole class is their average multiplie... | 5 | 4 | 4 | No Error | 90 | Core concept Average is not explained properly. |
M014 | GPT-4o | Avarage | Medium | The average of 8 numbers is 25. If one number, 32, is replaced by 20, find the new average. | New avarage is 23.5 | New avarage is 23.5 | Step 1: Find the original total of the 8 numbers.
Average = 25
Number of numbers = 8
Original total = 25 × 8
= 200
Step 2: Find the change in the total.
The number 32 is replaced by 20.
Decrease = 32 − 20
= 12
New total = 200 − 12
= 188
Step 3: Find the new average.
New average = 188 ÷ 8
= 23.5
Final Answer: 23.5 | 5 | 4 | 4 | No Error | 90 | Step 2 is not clear, repalcement of numerb concept is not explained properly. |
M014 | Claude | Avarage | Medium | The average of 8 numbers is 25. If one number, 32, is replaced by 20, find the new average. | New avarage is 23.5 | New avarage is 23.5 | Given:
- Average of 8 numbers = 25
- One number, 32, is removed and replaced by 20
- Find the new average.
Step 1: Find the original total sum of all 8 numbers
Total Sum = Average x Count
= 25 x 8
= 200
Step 2: Find the new total sum after the replacement
When 32 is replaced by 20:
- We REMOVE 32... | 5 | 5 | 5 | No Error | 100 | All steps are clearly shown |
M014 | Gemini | Avarage | Medium | The average of 8 numbers is 25. If one number, 32, is replaced by 20, find the new average. | New avarage is 23.5 | New avarage is 23.5 | Given information:
Total count of numbers = 8
Original average = 25
Number to be removed = 32
Number to be added = 20
Step 1: Calculate the original sum of the 8 numbers.
The sum is the average multiplied by the count of numbers.
Original sum = 25 x 8
Original sum = 200
Step 2: Calculate the new sum.
Subtract the num... | 5 | 5 | 4 | No Error | 96 | Missing clarity in concept and flow of explantion. |
M015 | GPT-4o | Avarage | Hard | The average weight of 15 people increases by 2 kg when a person weighing 60 kg is replaced by another person. Find the weight of the new person. | New person weight is 90 kg | New person weight is 90 kg | Step 1: Find the increase in the total weight.
Number of people = 15
Increase in average weight = 2 kg
Increase in total weight = 15 × 2
= 30 kg
Step 2: Find the weight of the new person.
The old person weighed 60 kg.
Since the total weight increased by 30 kg:
Weight of new person = 60 + 30
= 90 kg
Step 3: Verify.
Th... | 5 | 4 | 4 | No Error | 90 | Concept is not explaiend properly, missing clarity in the flow of reading, core points are missing. |
M015 | Claude | Avarage | Hard | The average weight of 15 people increases by 2 kg when a person weighing 60 kg is replaced by another person. Find the weight of the new person. | New person weight is 90 kg | New person weight is 90 kg | Given:
- Total number of people = 15
- A person weighing 60 kg is replaced by a new person
- The average weight INCREASES by 2 kg after the replacement
- Find the weight of the new person.
Step 1: Find the increase in total sum due to the replacement
When the average increases by 2 kg across 15 people, the total sum m... | 5 | 5 | 4 | No Error | 96 | Lengthy explanation creating mess |
M015 | Gemini | Avarage | Hard | The average weight of 15 people increases by 2 kg when a person weighing 60 kg is replaced by another person. Find the weight of the new person. | New person weight is 90 kg | New person weight is 90 kg | Given information:
Number of people = 15
Increase in average weight = 2 kg
Weight of the person being replaced = 60 kg
Step 1: Calculate the total increase in weight.
Since the average weight of all 15 people increases by 2 kg, the total weight of the group must have increased. To find this total increase, multiply th... | 5 | 4 | 4 | No Error | 90 | Missing clarity while reading in the flow |
M016 | GPT-4o | Profit & Loss | Easy | A shopkeeper buys an article for ₹800 and sells it for ₹920. Find the profit percentage. | profit precentage is 15% | profit precentage is 15% | Step 1: Identify the cost price and selling price.
Cost Price = ₹800
Selling Price = ₹920
Step 2: Find the profit.
Profit = Selling Price − Cost Price
= ₹920 − ₹800
= ₹120
Step 3: Calculate the profit percentage.
Profit Percentage = (Profit / Cost Price) × 100
= (120 / 800) × 100
= 15%
Final Answer: 15% profit. | 5 | 4 | 5 | No Error | 94 | Difference between Cost price and Selling price is not explained, and Profit formula is not explained. |
M016 | Claude | Profit & Loss | Easy | A shopkeeper buys an article for ₹800 and sells it for ₹920. Find the profit percentage. | profit precentage is 15% | profit precentage is 15% | Given:
- Cost Price (CP) = Rs. 800
- Selling Price (SP) = Rs. 920
- Find the profit percentage.
Step 1: Check whether there is a profit or a loss
Since Selling Price > Cost Price, the shopkeeper made a PROFIT.
Profit = Selling Price - Cost Price
= Rs. 920 - Rs. 800
= Rs. 120
Step 2: Apply the Profit ... | 5 | 5 | 5 | No Error | 100 | All steps are correctly explained. |
M016 | Gemini | Profit & Loss | Easy | A shopkeeper buys an article for ₹800 and sells it for ₹920. Find the profit percentage. | profit precentage is 15% | profit precentage is 15% | Given information:
Cost price of the article = 800 rupees
Selling price of the article = 920 rupees
Step 1: Calculate the profit amount.
The profit is the difference between the selling price and the cost price.
Profit = Selling price - Cost price
Profit = 920 - 800
Profit = 120 rupees
Step 2: Calculate the profit pe... | 5 | 4 | 4 | No Error | 90 | Rupees symbol is missing, im mathematics symbols are more prominent to use everytime otherthan words. Difference between cost price and selling is not expalined |
M017 | GPT-4o | Profit & Loss | Easy | An article costing ₹1,500 is sold at a loss of 12%. Find its selling price. | Selling Price is ₹1,320 | Selling Price is ₹1,320 | Step 1: Identify the cost price.
Cost Price = ₹1,500
Loss = 12%
Step 2: Find the loss amount.
Loss = 12% of ₹1,500
= (12/100) × 1,500
= ₹180
Step 3: Find the selling price.
Selling Price = Cost Price − Loss
= ₹1,500 − ₹180
= ₹1,320
Final Answer: ₹1,320. | 5 | 4 | 4 | No Error | 90 | Loss percentage formula is not mentioned, realtion between SP, CP and loss is given but not explained. |
M017 | Claude | Profit & Loss | Easy | An article costing ₹1,500 is sold at a loss of 12%. Find its selling price. | Selling Price is ₹1,320 | Selling Price is ₹1,320 | Given:
- Cost Price (CP) = Rs. 1,500
- Loss percentage = 12%
- Find the Selling Price (SP).
Step 1: Check the case
Since the article is sold at a LOSS, the selling price will be
LESS than the cost price.
Step 2: Calculate the Loss Amount
Loss Amount = (Loss % / 100) x Cost Price
= (12 / 100) x 1,500
... | 5 | 5 | 4 | No Error | 96 | Realtion between SP, CP and Loss is given but not explaiend properly. |
M017 | Gemini | Profit & Loss | Easy | An article costing ₹1,500 is sold at a loss of 12%. Find its selling price. | Selling Price is ₹1,320 | Selling Price is ₹1,320 | Given information:
Cost price of the article = 1500 rupees
Loss percentage = 12 percent
Step 1: Calculate the loss amount.
The loss amount is 12 percent of the cost price.
Loss = (12 / 100) x 1500
Loss = 0.12 x 1500
Loss = 180 rupees
Step 2: Calculate the selling price.
The selling price is the cost price minus the l... | 5 | 4 | 4 | No Error | 90 | Loss Precentage formula is not mentioned, realtion between SP, CP and loss is given but not explained. |
M018 | GPT-4o | Profit & Loss | Medium | A shopkeeper marks an article 25% above its cost price and gives a discount of 10%. Find the profit percentage. | Profit precentage is 12.5% | Profit precentage is 12.5% | Step 1: Assume the cost price is ₹100.
Step 2: The shopkeeper marks it 25% above the cost price.
Marked Price = ₹100 + 25% of ₹100
= ₹100 + ₹25
= ₹125
Step 3: A discount of 10% is given on the marked price.
Discount = 10% of ₹125
= ₹12.50
Step 4: Find the selling price.
Selling Price = ₹125 − ₹12.50
= ₹112.50
Step ... | 5 | 5 | 4 | No Error | 96 | Very step is clearly explained, but little bit clarity is missing |
M018 | Claude | Profit & Loss | Medium | A shopkeeper marks an article 25% above its cost price and gives a discount of 10%. Find the profit percentage. | Profit precentage is 12.5% | Profit precentage is 12.5% | Given:
- Article is marked 25% ABOVE its cost price
- A discount of 10% is given on the marked price
- Find the profit percentage.
Step 1: Assume a convenient cost price
Let Cost Price (CP) = Rs. 100
(Assuming Rs. 100 makes percentage calculations simple.)
Step 2: Find the Marked Price (MP)
The article is marked 25% ... | 5 | 5 | 4 | No Error | 96 | Lengthy explanation creates mess |
M018 | Gemini | Profit & Loss | Medium | A shopkeeper marks an article 25% above its cost price and gives a discount of 10%. Find the profit percentage. | Profit precentage is 12.5% | Profit precentage is 12.5% | Let the cost price of the article be 100 to make the calculations clear.
Step 1: Calculate the marked price.
The shopkeeper marks the article 25 percent above the cost price.
Markup amount = (25 / 100) x 100
Markup amount = 25
Marked price = Cost price + Markup amount
Marked price = 100 + 25 = 125
Step 2: Calculate t... | 5 | 4 | 4 | No Error | 90 | Using shortcuts like SP,CP will increase the understanding, writing everthing in theroy not looks like a maths |
M019 | GPT-4o | Profit & Loss | Medium | An article is sold for ₹1,440 at a profit of 20%. Find its cost price. | Cost price is ₹1200 | Cost price is ₹1200 | Step 1: Identify the selling price and profit percentage.
Selling Price = ₹1,440
Profit = 20%
Step 2: Understand the relationship.
If the cost price is 100%, then after a 20% profit:
Selling Price = 100% + 20% = 120% of Cost Price
So,
120% of Cost Price = ₹1,440
Step 3: Find the cost price.
Cost Price = (₹1,440 × 100... | 5 | 4 | 4 | No Error | 90 | Step 2 is not clear, by taking 100% of Cost price not expalined why? |
M019 | Claude | Profit & Loss | Medium | An article is sold for ₹1,440 at a profit of 20%. Find its cost price. | Cost price is ₹1200 | Cost price is ₹1200 | Given:
- Selling Price (SP) = Rs. 1,440
- Profit percentage = 20%
- Find the Cost Price (CP).
Step 1: Recall the relationship between SP, CP and Profit
SP = CP + Profit
SP = CP + (Profit % / 100) x CP
SP = CP x (1 + Profit % / 100)
Step 2: Understand what the selling price represents
A profit of 20% means the shopke... | 5 | 5 | 5 | No Error | 100 | All formulas and realtions are correctly established |
M019 | Gemini | Profit & Loss | Medium | An article is sold for ₹1,440 at a profit of 20%. Find its cost price. | Cost price is ₹1200 | Cost price is ₹1200 | Given information:
Selling price of the article = 1440 rupees
Profit percentage = 20 percent
Step 1: Understand the relationship between cost price and selling price.
The selling price is equal to the cost price plus the profit amount.
Since the profit is 20 percent of the cost price, the selling price represents 100 ... | 5 | 4 | 4 | No Error | 90 | Using symbols and shorcut will make maths more visual, than words. Calculation part is not clear |
M020 | GPT-4o | Profit & Loss | Hard | A dishonest shopkeeper claims to sell goods at cost price but uses a 900 g weight instead of 1 kg. Find his gain percentage. | Gain precnetage is 11.111 % (or) 11 1/9 % | Gain precnetage is 11.111 % (or) 11 1/9 % | Step 1: Assume the cost price of 1 kg of goods is ₹100.
So, the cost price of 900 g is:
₹100 × 900/1000 = ₹90
Step 2: The shopkeeper claims to sell 1 kg at cost price.
Therefore, he charges ₹100 for what is actually only 900 g.
Selling price of 900 g = ₹100
Cost price of 900 g = ₹90
Step 3: Find the gain.
Gain = Sell... | 5 | 4 | 3 | No Error | 86 | Core concept of wrong weights is not expalined at first |
M020 | Claude | Profit & Loss | Hard | A dishonest shopkeeper claims to sell goods at cost price but uses a 900 g weight instead of 1 kg. Find his gain percentage. | Gain precnetage is 11.111 % (or) 11 1/9 % | Gain precnetage is 11.111 % (or) 11 1/9 % | Given:
- The shopkeeper claims to sell 1 kg (1,000 g) of goods.
- He actually gives only 900 g instead of 1,000 g.
- He charges the customer at cost price (for 1,000 g).
- Find the gain percentage.
Step 1: Understand what is actually happening
The shopkeeper collects PAYMENT for 1,000 g but delivers
only 900 g. So he ... | 5 | 5 | 4 | No Error | 96 | All stpes are clear but lengthy answer missing clarity |
M020 | Gemini | Profit & Loss | Hard | A dishonest shopkeeper claims to sell goods at cost price but uses a 900 g weight instead of 1 kg. Find his gain percentage. | Gain precnetage is 11.111 % (or) 11 1/9 % | Gain precnetage is 11.111 % (or) 11 1/9 % | Let the cost price of 1 gram of the goods be 1 rupee.
Step 1: Determine the cost price of the goods actually given.
The shopkeeper uses a 900 gram weight instead of a full kilogram.
Actual cost price of the 900 grams given to the customer = 900 rupees.
This is the actual cost incurred by the shopkeeper.
Step 2: Deter... | 5 | 4 | 3 | No Error | 86 | Theory like visualization not looking like maths and missing core concept and clarity. |
M021 | GPT-4o | Simple & Compound Interest | Easy | ₹5,000 is lent at 8% simple interest per annum for 2 years. Find the simple interest. | Simple interest is ₹800 | Simple interest is ₹800 | Step 1: Identify the given values.
Principal = ₹5,000
Rate = 8% per annum
Time = 2 years
Step 2: Use the simple interest formula.
Simple Interest = (Principal × Rate × Time) / 100
Step 3: Substitute the values.
Simple Interest = (5,000 × 8 × 2) / 100
= 80,000 / 100
= ₹800
Final Answer: ₹800. | 5 | 4 | 5 | No Error | 94 | Simple interest terms are not expaliend |
M021 | Claude | Simple & Compound Interest | Easy | ₹5,000 is lent at 8% simple interest per annum for 2 years. Find the simple interest. | Simple interest is ₹800 | Simple interest is ₹800 | Given:
- Principal (P) = Rs. 5,000
- Rate of Interest (R) = 8% per annum
- Time (T) = 2 years
- Find the Simple Interest (SI).
Step 1: Recall the Simple Interest formula
Simple Interest (SI) = (P x R x T) / 100
Where:
P = Principal (the original sum lent or borrowed)
R = Rate (interest... | 5 | 5 | 5 | No Error | 100 | All steps are correctly explained. |
M021 | Gemini | Simple & Compound Interest | Easy | ₹5,000 is lent at 8% simple interest per annum for 2 years. Find the simple interest. | Simple interest is ₹800 | Simple interest is ₹800 | Given information:
Principal = 5000 rupees
Rate of interest = 8 percent per annum
Time = 2 years
Step 1: State the formula for simple interest.
Simple Interest = (Principal x Rate x Time) / 100
Step 2: Substitute the given values into the formula.
Simple Interest = (5000 x 8 x 2) / 100
Step 3: Perform the calculatio... | 5 | 4 | 5 | No Error | 94 | Simple interest terms are not expaliend |
M022 | GPT-4o | Simple & Compound Interest | Medium | Find the amount on ₹8,000 at 10% compound interest per annum for 2 years. | Total amount is ₹9,680 | Total amount is ₹9,680 | Step 1: Identify the given values.
Principal = ₹8,000
Rate = 10% per annum
Time = 2 years
Step 2: Calculate the amount after the first year.
Interest for 1st year = 10% of ₹8,000
= ₹800
Amount after 1st year = ₹8,000 + ₹800
= ₹8,800
Step 3: Calculate the interest for the second year.
Interest for 2nd year = 10% of ₹8... | 5 | 4 | 4 | No Error | 90 | Compound interest concept is not exaplined properly, amd calculation is also not clear. |
M022 | Claude | Simple & Compound Interest | Medium | Find the amount on ₹8,000 at 10% compound interest per annum for 2 years. | Total amount is ₹9,680 | Total amount is ₹9,680 | Given:
- Principal (P) = Rs. 8,000
- Rate of Interest (R) = 10% per annum
- Time (T) = 2 years
- Compounding = Annually (once per year)
- Find the Compound Interest (CI) and Total Amount.
Step 1: Recall the Compound Interest formula
Amount (A) = P x (1 + R / 100) ^ T
Where:
P = Principal
R... | 5 | 5 | 4 | No Error | 96 | lengthy answer missing clarity. |
M022 | Gemini | Simple & Compound Interest | Medium | Find the amount on ₹8,000 at 10% compound interest per annum for 2 years. | Total amount is ₹9,680 | Total amount is ₹9,680 | Given information:
Principal = 8000 rupees
Rate of interest = 10 percent per annum
Time = 2 years
Step 1: State the formula for the amount under compound interest.
Amount = Principal x (1 + Rate / 100)^Time
(where Time is in years)
Step 2: Substitute the given values into the formula.
Amount = 8000 x (1 + 10 / 100)^2... | 5 | 5 | 4 | No Error | 96 | Calculation part is not explained correctly. |
M023 | GPT-4o | Simple & Compound Interest | Medium | Find the difference between compound interest and simple interest on ₹10,000 at 10% per annum for 2 years. | Difference of CI and SI is ₹100 | Difference of CI and SI is ₹100 | Principal = ₹10,000
Rate = 10% per annum
Time = 2 years
Step 1: Find Simple Interest
SI = (P × R × T) / 100
SI = (10,000 × 10 × 2) / 100
SI = ₹2,000
Step 2: Find Compound Interest
For 2 years:
Amount = P × (1 + R/100)^T
Amount = 10,000 × (1 + 10/100)^2
Amount = 10,000 × 1.1 × 1.1
Amount = ₹12,100
Compound Interest =... | 5 | 4 | 4 | No Error | 90 | Simple interest and compound interest terms are not expaliend, and calculation part is not clear. |
M023 | Claude | Simple & Compound Interest | Medium | Find the difference between compound interest and simple interest on ₹10,000 at 10% per annum for 2 years. | Difference of CI and SI is ₹100 | Difference of CI and SI is ₹100 | Given:
- Principal (P) = Rs. 10,000
- Rate of Interest (R) = 10% per annum
- Time (T) = 2 years
- Find the difference between CI and SI.
Step 1: Calculate Simple Interest (SI)
SI = (P x R x T) / 100
= (10,000 x 10 x 2) / 100
= 2,00,000 / 100
= Rs. 2,000
Step 2: Calculate Compound Interest ... | 5 | 5 | 4 | No Error | 96 | lengthy answer missing clarity. |
M023 | Gemini | Simple & Compound Interest | Medium | Find the difference between compound interest and simple interest on ₹10,000 at 10% per annum for 2 years. | Difference of CI and SI is ₹100 | Difference of CI and SI is ₹100 | Given information:
Principal = 10000 rupees
Rate of interest = 10 percent per annum
Time = 2 years
Step 1: Calculate the simple interest.
Simple Interest = (Principal x Rate x Time) / 100
Simple Interest = (10000 x 10 x 2) / 100
Simple Interest = 200000 / 100
Simple Interest = 2000 rupees
Step 2: Calculate the compou... | 5 | 4 | 4 | No Error | 90 | Calculation part is not clear. |
M024 | GPT-4o | Simple & Compound Interest | Hard | A sum amounts to ₹13,310 in 3 years at 10% compound interest per annum. Find the principal. | Principal amount is ₹10,000 | Principal amount is ₹10,000 | Given:
Amount = ₹13,310
Rate = 10% per annum
Time = 3 years
We know:
Amount = Principal × (1 + Rate/100)^Time
Step 1: Substitute the values
13,310 = Principal × (1 + 10/100)^3
13,310 = Principal × (1.1)^3
Step 2: Calculate 1.1³
1.1 × 1.1 × 1.1 = 1.331
So,
13,310 = Principal × 1.331
Step 3: Find the principal
Princ... | 5 | 4 | 3 | No Error | 86 | Core concept and calculation part is not clear |
M024 | Claude | Simple & Compound Interest | Hard | A sum amounts to ₹13,310 in 3 years at 10% compound interest per annum. Find the principal. | Principal amount is ₹10,000 | Principal amount is ₹10,000 | Given:
- Amount (A) = Rs. 13,310
- Rate of Interest (R) = 10% per annum
- Time (T) = 3 years
- Compounding = Annually
- Find the Principal (P).
Step 1: Recall the Compound Interest formula
Amount (A) = P x (1 + R / 100) ^ T
Here we need to work BACKWARDS from Amount to find Principal... | 5 | 4 | 4 | No Error | 90 | lengthy answer missing clarity. Formula notation is written properly. |
M024 | Gemini | Simple & Compound Interest | Hard | A sum amounts to ₹13,310 in 3 years at 10% compound interest per annum. Find the principal. | Principal amount is ₹10,000 | Principal amount is ₹10,000 | Given information:
Amount = 13310 rupees
Rate of interest = 10 percent per annum
Time = 3 years
Step 1: State the formula for the amount under compound interest.
Amount = Principal x (1 + Rate / 100)^Time
Step 2: Substitute the given values into the formula.
13310 = Principal x (1 + 10 / 100)^3
Step 3: Simplify the ... | 5 | 4 | 4 | No Error | 90 | Missing concept explanation |
M025 | GPT-4o | Simple & Compound Interest | Hard | The compound interest on a certain sum for two years at 12% per annum is ₹2,544. Find the principal. | Principal amount is ₹10,000 | Principal amount is ₹10,000 | Given:
Compound Interest = ₹2,544
Rate = 12% per annum
Time = 2 years
Step 1: Use the compound interest formula
For 2 years:
CI = P × [(1 + R/100)^2 − 1]
Step 2: Substitute the values
2,544 = P × [(1 + 12/100)^2 − 1]
2,544 = P × [(1.12)^2 − 1]
Step 3: Calculate 1.12²
1.12 × 1.12 = 1.2544
Therefore:
2,544 = P × (1.2... | 5 | 4 | 4 | No Error | 90 | Calculation part is not clear. |
M025 | Claude | Simple & Compound Interest | Hard | The compound interest on a certain sum for two years at 12% per annum is ₹2,544. Find the principal. | Principal amount is ₹10,000 | Principal amount is ₹10,000 | Given:
- Compound Interest (CI) = Rs. 2,544
- Rate of Interest (R) = 12% per annum
- Time (T) = 2 years
- Find the Principal (P).
Step 1: Recall the Compound Interest formula
CI = P x [(1 + R / 100) ^ T - 1]
We know CI, R and T. We need to find P.
Rearranging:
P = CI / [(1 + R / 100) ^ T - 1]
Step 2: ... | 5 | 4 | 4 | No Error | 90 | Calculation part is not clear. |
M025 | Gemini | Simple & Compound Interest | Hard | The compound interest on a certain sum for two years at 12% per annum is ₹2,544. Find the principal. | Principal amount is ₹10,000 | Principal amount is ₹10,000 | Given information:
Compound interest = 2544 rupees
Rate of interest = 12 percent per annum
Time = 2 years
Step 1: State the formula for compound interest.
Compound Interest = Principal x [(1 + Rate / 100)^Time - 1]
Step 2: Substitute the given values into the formula.
2544 = Principal x [(1 + 12 / 100)^2 - 1]
Step 3... | 5 | 4 | 4 | No Error | 90 | Too short and calculation part is not clear. |
M026 | GPT-4o | Time & Work | Easy | A can complete a work in 10 days and B can complete the same work in 15 days. How many days will they take working together? | 6 days | 6 days | Given:
A can complete the work in 10 days.
B can complete the work in 15 days.
Step 1: Find A's one-day work
A's 1-day work = 1/10
Step 2: Find B's one-day work
B's 1-day work = 1/15
Step 3: Add their daily work
Together's 1-day work = 1/10 + 1/15
LCM of 10 and 15 = 30
= 3/30 + 2/30
= 5/30
= 1/6
So, together they c... | 5 | 4 | 5 | No Error | 94 | Realtion between TIme and work done is established exaplined. |
M026 | Claude | Time & Work | Easy | A can complete a work in 10 days and B can complete the same work in 15 days. How many days will they take working together? | 6 days | 6 days | Given:
- A can complete the work in 10 days.
- B can complete the work in 15 days.
- Find the number of days taken when A and B work together.
Step 1: Find the one-day work of A
A completes the full work in 10 days.
A's one-day work = 1 / 10
(A finishes 1/10th of the total work each day.)
Step 2: Find the one-day wo... | 5 | 4 | 5 | No Error | 94 | Explaining concept at the starting can imporve understand better. |
M026 | Gemini | Time & Work | Easy | A can complete a work in 10 days and B can complete the same work in 15 days. How many days will they take working together? | 6 days | 6 days | Given information:
Time taken by A to complete the work = 10 days
Time taken by B to complete the work = 15 days
Step 1: Calculate the amount of work A can do in one day.
Since A takes 10 days to complete the entire work, the portion of the work A does in one day is 1 / 10.
Step 2: Calculate the amount of work B can ... | 5 | 4 | 4 | No Error | 90 | Core concept is not clear and total messy explanation. |
M027 | GPT-4o | Time & Work | Easy | A can complete a work in 12 days. What fraction of the work can A complete in one day? | 1/12 of work completes in one day | 1/12 of work completes in one day | Given:
A can complete the work in 12 days.
Step 1: Understand the meaning
If A takes 12 days to complete the whole work, then in 1 day A will complete 1/12 of the work.
Step 2: Write the fraction
One-day work of A = 1/12
Final Answer: 1/12 of the work in one day. | 5 | 4 | 5 | No Error | 94 | Concept is not explained. |
M027 | Claude | Time & Work | Easy | A can complete a work in 12 days. What fraction of the work can A complete in one day? | 1/12 of work completes in one day | 1/12 of work completes in one day | Given:
- A can complete the full work in 12 days.
- Find the fraction of work A can complete in one day.
Step 1: Understand the core concept
If a person completes the FULL work in a given number of days,
then in ONE day they complete ONE part out of the total number
of days. This is the basic principle of work proble... | 5 | 5 | 5 | No Error | 100 | All stpes and reasoning are clear. |
M027 | Gemini | Time & Work | Easy | A can complete a work in 12 days. What fraction of the work can A complete in one day? | 1/12 of work completes in one day | 1/12 of work completes in one day | Given information:
Time taken by A to complete the entire work = 12 days
Step 1: Understand the relationship between total time and work done per day.
If a person can complete a full piece of work in a certain number of days, the amount of work they do in exactly one day is the reciprocal of that total number of days.... | 5 | 5 | 5 | No Error | 100 | Simple and more understandable. |
M028 | GPT-4o | Time & Work | Medium | A and B can complete a work together in 8 days. A alone can complete it in 12 days. How many days will B alone take? | B Completes work in 24 days | B Completes work in 24 days | Given:
A and B together can complete the work in 8 days.
A alone can complete the work in 12 days.
Step 1: Find A and B's one-day work
Together's 1-day work = 1/8
Step 2: Find A's one-day work
A's 1-day work = 1/12
Step 3: Find B's one-day work
B's 1-day work = Together's work − A's work
= 1/8 − 1/12
LCM of 8 and 1... | 5 | 4 | 4 | No Error | 90 | Core concept is not explained properly. |
M028 | Claude | Time & Work | Medium | A and B can complete a work together in 8 days. A alone can complete it in 12 days. How many days will B alone take? | B Completes work in 24 days | B Completes work in 24 days | Given:
- A and B together complete the work in 8 days.
- A alone can complete the work in 12 days.
- Find the number of days B alone will take.
Step 1: Find the combined one-day work of A and B
A and B together finish the work in 8 days.
(A + B)'s one-day work = 1 / 8
Step 2: Find A's one-day work
A alone finishes th... | 5 | 4 | 3 | No Error | 86 | Core concept is not explained properly. Lengthy answer not understandable. |
M028 | Gemini | Time & Work | Medium | A and B can complete a work together in 8 days. A alone can complete it in 12 days. How many days will B alone take? | B Completes work in 24 days | B Completes work in 24 days | Given information:
Time taken by A and B together to complete the work = 8 days
Time taken by A alone to complete the work = 12 days
Step 1: Calculate the combined work A and B can do in one day.
Since A and B take 8 days to complete the entire work, the portion of the work they do together in one day is 1 / 8.
Step ... | 5 | 4 | 4 | No Error | 90 | Concept is not explained fully. |
M029 | GPT-4o | Time & Work | Medium | A can complete a work in 20 days and B in 30 days. They work together for 6 days. What fraction of the work remains? | 1/2 works remains | 1/2 works remains | Given:
A can complete the work in 20 days.
B can complete the work in 30 days.
They work together for 6 days.
Step 1: Find A's one-day work
A's 1-day work = 1/20
Step 2: Find B's one-day work
B's 1-day work = 1/30
Step 3: Find their combined one-day work
Together's 1-day work = 1/20 + 1/30
LCM of 20 and 30 = 60
= 3/... | 5 | 4 | 4 | null | 90 | Core concept is missing in explanation |
M029 | Claude | Time & Work | Medium | A can complete a work in 20 days and B in 30 days. They work together for 6 days. What fraction of the work remains? | 1/2 works remains | 1/2 works remains | Given:
- A can complete the work in 20 days.
- B can complete the work in 30 days.
- They work TOGETHER for 6 days.
- Find the fraction of work that remains.
Step 1: Find A's one-day work
A completes the full work in 20 days.
A's one-day work = 1 / 20
Step 2: Find B's one-day work
B completes the full work in 30 da... | 5 | 4 | 5 | No Error | 94 | Explaining concept with steps is correct way of doing maths but it is missing. |
M029 | Gemini | Time & Work | Medium | A can complete a work in 20 days and B in 30 days. They work together for 6 days. What fraction of the work remains? | 1/2 works remains | 1/2 works remains | Given information:
Time taken by A to complete the work = 20 days
Time taken by B to complete the work = 30 days
Time they work together = 6 days
Step 1: Calculate the work A can do in one day.
Since A takes 20 days to complete the entire work, the portion of the work A does in one day is 1 / 20.
Step 2: Calculate th... | 5 | 4 | 3 | No Error | 86 | Lengthy and messy text |
M030 | GPT-4o | Time & Work | Hard | A, B and C can complete a work individually in 12, 15 and 20 days respectively. If they work together for 4 days, what fraction of the work remains? | 1/5 work remains | 1/5 work remains | Given:
A can complete the work in 12 days.
B can complete the work in 15 days.
C can complete the work in 20 days.
They work together for 4 days.
Step 1: Find each person's one-day work
A's 1-day work = 1/12
B's 1-day work = 1/15
C's 1-day work = 1/20
Step 2: Find their combined one-day work
Together's 1-day work = ... | 5 | 4 | 5 | No Error | 94 | Concept is not explained |
M030 | Claude | Time & Work | Hard | A, B and C can complete a work individually in 12, 15 and 20 days respectively. If they work together for 4 days, what fraction of the work remains? | 1/5 work remains | 1/5 work remains | Given:
- A can complete the work in 12 days.
- B can complete the work in 15 days.
- C can complete the work in 20 days.
- They ALL work together for 4 days.
- Find the fraction of work that remains.
Step 1: Find the one-day work of each person
A's one-day work = 1 / 12
B's one-day work = 1 / 15
C's one-day work = 1 /... | 5 | 5 | 4 | No Error | 96 | Answer is clear but lengthy answer is messy to understand fastly |
M030 | Gemini | Time & Work | Hard | A, B and C can complete a work individually in 12, 15 and 20 days respectively. If they work together for 4 days, what fraction of the work remains? | 1/5 work remains | 1/5 work remains | Given information:
Time taken by A to complete the work = 12 days
Time taken by B to complete the work = 15 days
Time taken by C to complete the work = 20 days
Time they work together = 4 days
Step 1: Calculate the work A, B, and C can each do in one day.
Portion of work A does in one day = 1 / 12
Portion of work B do... | 5 | 4 | 4 | No Error | 90 | Calculation part is not celar, concept is also not explained. |
M031 | GPT-4o | TIme, Speed & Distance | Easy | A car travels 240 km at a speed of 60 km/h. How much time does it take? | Time taken by car is 4 hours | Time taken by car is 4 hours | Given:
Distance = 240 km
Speed = 60 km/h
Step 1: Use the time formula
Time = Distance / Speed
Step 2: Substitute the values
Time = 240 / 60
Time = 4 hours
Final Answer: 4 hours | 5 | 3 | 4 | No Error | 84 | Short and sweet but concept is not explained at the starting of the answer. |
M031 | Claude | TIme, Speed & Distance | Easy | A car travels 240 km at a speed of 60 km/h. How much time does it take? | Time taken by car is 4 hours | Time taken by car is 4 hours | Given:
- Distance = 240 km
- Speed = 60 km/h
- Find the Time taken.
Step 1: Recall the Speed, Distance and Time formula
The three key formulas to remember:
Time = Distance / Speed
Distance = Speed x Time
Speed = Distance / Time
A simple triangle to remember:
D
-... | 5 | 5 | 5 | No Error | 100 | All the steps and concepts are clear. |
M031 | Gemini | TIme, Speed & Distance | Easy | A car travels 240 km at a speed of 60 km/h. How much time does it take? | Time taken by car is 4 hours | Time taken by car is 4 hours | Given information:
Distance traveled = 240 km
Speed of the car = 60 km/h
Step 1: State the formula for time.
Time = Distance / Speed
Step 2: Substitute the given values into the formula.
Time = 240 / 60
Step 3: Calculate the time taken.
Divide the distance by the speed.
Time = 4 hours
Final Answer:
The car takes 4 ... | 5 | 4 | 4 | No Error | 90 | answer is clear but concept is missing |
M032 | GPT-4o | TIme, Speed & Distance | Easy | A train travels at 72 km/h. Convert its speed into metres per second. | 20 m/s | 20 m/s | Given:
Speed = 72 km/h
Step 1: Convert kilometres into metres
1 kilometre = 1000 metres
So,
72 km = 72 × 1000 = 72,000 metres
Step 2: Convert hours into seconds
1 hour = 60 × 60 = 3600 seconds
Therefore,
72 km/h = 72,000/3600 m/s
Step 3: Simplify
72,000 ÷ 3600 = 20
Final Answer: 20 m/s | 5 | 5 | 5 | No Error | 100 | All the steps are clear. |
M032 | Claude | TIme, Speed & Distance | Easy | A train travels at 72 km/h. Convert its speed into metres per second. | 20 m/s | 20 m/s | Given:
- Speed of train = 72 km/h
- Convert from km/h to m/s.
Step 1: Understand what needs to be converted
km/h means kilometres per hour.
m/s means metres per second.
To convert km/h into m/s, we need to convert:
- kilometres into metres (larger unit to smaller unit)
- hours into seconds (smaller unit... | 5 | 5 | 3 | No Error | 92 | Too Lengthy is no need for this question. |
M032 | Gemini | TIme, Speed & Distance | Easy | A train travels at 72 km/h. Convert its speed into metres per second. | 20 m/s | 20 m/s | Given information:
Speed of the train = 72 km/h
Step 1: Understand the conversion factors.
1 kilometre = 1000 metres
1 hour = 60 minutes, and 1 minute = 60 seconds, so 1 hour = 60 x 60 = 3600 seconds
Step 2: Establish the conversion ratio.
To convert a speed from kilometres per hour to metres per second, multiply by ... | 5 | 4 | 3 | No Error | 86 | Step 2 is not conveyed properly in calculation. |
M033 | GPT-4o | TIme, Speed & Distance | Medium | A man travels 60 km at 30 km/h and another 60 km at 60 km/h. Find his average speed for the entire journey. | Average speed is 40 km/h | Average speed is 40 km/h | Given:
First distance = 60 km
First speed = 30 km/h
Second distance = 60 km
Second speed = 60 km/h
Step 1: Find the time taken for the first 60 km
Time = Distance / Speed
= 60 / 30
= 2 hours
Step 2: Find the time taken for the second 60 km
Time = 60 / 60
= 1 hour
Step 3: Find total distance
Total distance = 60 + 60... | 5 | 5 | 4 | No Error | 96 | Concept is not explaiend at starting, missing clarity in the existing concept. |
M033 | Claude | TIme, Speed & Distance | Medium | A man travels 60 km at 30 km/h and another 60 km at 60 km/h. Find his average speed for the entire journey. | Average speed is 40 km/h | Average speed is 40 km/h | Given:
- First leg : Distance = 60 km, Speed = 30 km/h
- Second leg : Distance = 60 km, Speed = 60 km/h
- Find the average speed for the entire journey.
Step 1: Recall the correct formula for average speed
Average Speed = Total Distance / Total Time
IMPORTANT: Average speed is NEVER simply the arithmetic
mean (sum o... | 5 | 5 | 4 | No Error | 96 | Too Lengthy and used misunderstanding words. |
M033 | Gemini | TIme, Speed & Distance | Medium | A man travels 60 km at 30 km/h and another 60 km at 60 km/h. Find his average speed for the entire journey. | Average speed is 40 km/h | Average speed is 40 km/h | Given information:
Distance of the first part of the journey = 60 km
Speed during the first part = 30 km/h
Distance of the second part of the journey = 60 km
Speed during the second part = 60 km/h
Step 1: Calculate the time taken for the first part of the journey.
Time is calculated by dividing distance by speed.
Time... | 5 | 5 | 5 | No Error | 100 | All the steps are clear and understandable. |
M034 | GPT-4o | TIme, Speed & Distance | Medium | A train 150 m long is moving at 54 km/h. How long will it take to cross a pole? | 10 seconds to cross a pole | 10 seconds to cross a pole | Given:
Length of train = 150 m
Speed = 54 km/h
Step 1: Convert speed into metres per second
54 km/h = 54 × 5/18 m/s
= 15 m/s
Step 2: Understand the distance covered
When a train crosses a pole, it needs to cover a distance equal to its own length.
Distance = 150 m
Step 3: Find the time
Time = Distance / Speed
= 150 ... | 5 | 4 | 4 | No Error | 90 | Concept is not clear. in step2 |
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language: - en tags: - math - llm-evaluation - benchmarking - annotation size_categories: - n<1K
LLM Math Response Evaluation Dataset
Dataset Summary
A human-annotated dataset of 150 AI-generated math responses evaluated across GPT-4o, Claude, and Gemini. Each response is scored on Correctness, Reasoning, and Clarity using a structured rubric, with written justification for every score.
Supported Tasks
- LLM evaluation and benchmarking
- Math reasoning quality assessment
- Error type classification in AI responses
Dataset Structure
150 rows × 14 columns 50 unique math problems × 3 LLMs
Scoring
Final Score = (Correctness x 0.5 + Reasoning x 0.3 + Clarity x 0.2) x 20 → scale of 0 to 100
Source
Problems sourced from standard competitive exam question banks. Responses collected and evaluated manually in [Month Year].
Author
N B V BHARATH GitHub: github.com/nbvbharath-1729/llm-math-evaluation-dataset
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