mathewhe/aqua_rat huggingface dataset:
Question: A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 4680, what will be A's share of the earnings?
(A) $1100
(B) $520
(C) $2080
(D) $1170
(E) $630
Rationale: Explanatory Answer
A, B and C will share the amount of $4680 in the ratio of the amounts of work done by them.
As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.
Similarly, B will complete 1/8th and C will complete 1/12th of the work.
So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12
Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.
We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.
i.e., the ratio in which A : B : C will share $4680 will be 4 : 3 : 2.
Hence, A's share will be 4*4680/9 =2080.
correct choice is (C)
Answer: (C) $2080
Question: d.	What will the number XI represent in the below sequence?
1296, 432, 216, 216, 72, 36, 36, 12, 6, 6, XI
(A) 0
(B) 1
(C) 4
(D) 3
(E) 2
Rationale: The sequence progresses Ã·3, Ã·2, Ã·1 repeated; the number XI is 6 Ã·3 = 2.
Ans E = 2
Answer: (E) 2
Question: How many terms are there in 2, 4, 8, 16,..., 4096?
(A) 14
(B) 11
(C) 12
(D) 10
(E) 8
Rationale: 2, 4, 8, 16, ..., 4096 is a G.P with a =2
and r =4/2 =2
Let the number of terms be n. Then
2 x 2 ^n-1 = 4096
or 2^n-1 = 2048 = 2^11
Thus n - 1 =11
n= 12
ANSWER:C
Answer: (C) 12
Question: If the cost price of 50 articles is equal to the selling price of 35 articles, then the gain or loss percent is?
(A) 16
(B) 127
(C) 12
(D) 18
(E) 43
Rationale: Percentage of profit = 15/35 * 100 = 43%
Answer: E
Answer: (E) 43
Question: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?
(A) 20
(B) 19
(C) 18
(D) 17
(E) 16
Rationale: Lets Q's first number be 14
As per question, Q contains 9 multiples of 14 , so let Q's last number be 126. (14∗9)
We have,
a n = a+(n−1)d
Then
126 = 14 + (n-1)7
Solving for n , we get n = 17
ANSWER:D
Answer: (D) 17
Question: The length of a rectangle is 3 times its width. If the width of the rectangle is 5 inches, what is the rectangle's area, in square inches?
(A) 30 square inches
(B) 75 square inches
(C) 68 square inches
(D) 89 square inches
(E) 92 square inches
Rationale: If the width is 5 in and the length is 3 times the width, then the length is
3 * 5 = 15 in
The area is given by
5 * 15 = 75 square inches
correct answer B
Answer: (B) 75 square inches
Question: A speed of 20 metres per second is the same as :
(A) 72 km/hr
(B) 66 km/hr
(C) 60 km/hr
(D) 77.5 km/hr
(E) None
Rationale: Sol.
20 m/sec = [20 * 18/5] km/hr = 72 km/hr.
Answer A
Answer: (A) 72 km/hr
Question: A vase has 2 dozens of assorted flowers of daisies and roses. If the daisies are twice more than the roses. How many roses are in it?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 16
Rationale: Let the daisies be x
Roses is twice more than roses = 2x
x + 2x = 24
3x = 24
X =24/3 = 8
Roses is 2x = 2 * 8 = 16
ANSWER: E
Answer: (E) 16
Question: If x^4 + y^4 = 1300, then the greatest possible value of x is between:
(A) 1 to 2
(B) 2 to 3
(C) 3 to 4
(D) 4 to 5
(E) 6 to 7
Rationale: The answers to this question provide a great 'hint' as to how to go about solving it; since they're all essentially 'ranges', you can use them to figure out which solution contains the maximum value of X.
We're told that X^4 + Y^4 = 1300. To maximize the value of X, we need to minimize the value of Y^4. The smallest that Y^4 could be is 0 (when Y = 0), so we'll have....
X^4 = 1300
Looking at the answers, it makes sense to see what 6^4 equals....
6^4 = 1296
Since that is BELOW 1300, and 7^4 will clearly be MORE than 1300, we have the correct answer.
Final Answer:
E
Answer: (E) 6 to 7
Question: simplify : 3x - 5 + 23x - 9
(A) 2(14x-9)
(B) 2(13x-7)
(C) (14-5x)
(D) 2(10-7x)
(E) 2x(14-7)
Rationale: 3x -5 +23x-9 , = 3x+23x - 5 - 9
= 26x - 14, = 2(13x - 7). correct answer : (B)
Answer: (B) 2(13x-7)
Question: A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.
(A) 252
(B) 240
(C) 300
(D) 340
(E) None
Rationale: Solution:
Since, there are 5 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is,
[10!/(5!�5!)]= 252
Answer: Option A
Answer: (A) 252
Question: A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 7000 as profit , what is their total profit?
(A) 28000
(B) 30000
(C) 32000
(D) 34000
(E) 49000
Rationale: Explanation :
Suppose B's investment = x. Then A's investment= 3x
Suppose Bs period of investment = y, then A's period of investment = 2y
A : B = 3x * 2y : xy
= 6 : 1
Total profit * 1/7 = 7000
=> Total profit = 7000*7 = 49000. Answer : Option E
Answer: (E) 49000
Question: A fort of 5000 soldiers has provisions for 125 days. After 25 days some of them left and the food was now enough for the same period of 125 days as before. How many of them left?
(A) 900
(B) 1000
(C) 1100
(D) 1200
(E) 1300
Rationale: 2000 ---- 50
5000 ---- 100
x ----- 125
x*125 = 5000*100
x=4000
5000
-------
1000
Answer: B
Answer: (B) 1000
Question: A, B and C enter into a partnership. They invest Rs. 90,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?
(A) 12 : 3 : 4
(B) 23 : 2 : 4
(C) 22: 2 : 1
(D) 27: 16 : 28
(E) none
Rationale: Sol.
A : B : C = (40000 * 36) : (80000 * 12 + 40000 * 24)
: (120000 * 24 + 40000 * 12) =324 : 192 : 336 = 27 : 16 : 28
Answer D
Answer: (D) 27: 16 : 28
Question: A boy has 9 trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
(A) 100
(B) 102
(C) 104
(D) 108
(E) 110
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
D
Answer: (D) 108
Question: If a#b = ab – b + b^2, then 2#3 =
(A) 2
(B) 8
(C) 12
(D) 21
(E) 35
Rationale: Solution -
Simply substitute 2 and 3 in equation in the place of a and b respectively.
2#3 = 2*3 - 3 + 3^2 = 6 - 3 + 9 = 12. ANS C
Answer: (C) 12
Question: A certain company charges $15 per package to ship packages weighing less than 3 pounds each. For a package weighing 3 pounds or more, the company charges an initial fee of $15 plus $3 per pound. If the company charged $60 to ship a certain package, which of the following was the weight of the package, in pounds?
(A) 12
(B) 13
(C) 20
(D) 25
(E) 15
Rationale: Let the weight of the package be X. Then the cost is 3*X + 15= 60 ---> 3X=45 ---> X=15
Answer : E
Answer: (E) 15
Question: A man’s speed with the current is 19 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is :
(A) 8.5 km/hr
(B) 9.5 km/hr
(C) 10 km/hr
(D) 14 km/hr
(E) None of these
Rationale: Solution
Man's rate in still water = (19-2.5) km/hr = 16.5 km/hr.
Man's rate against the current = (16.5-2.5) km/hr = 14 km/hr Answer D
Answer: (D) 14 km/hr
Question: 10 x 1.8 - 2 x 1.5/0.3 = ?
(A) 30
(B) 20
(C) 15
(D) 44
(E) 50
Rationale: Given Expression
= (18 - 3.0)/0.3
= 15/0.3
= 150/3
= 50
Answer is E.
Answer: (E) 50
Question: The least number, which when divided by 8, 15, 20 and 54 leaves in each case a remainder of 8 is:
(A) 448
(B) 488
(C) 542
(D) 548
(E) 1088
Rationale: Required number = (L.C.M. of 8, 15, 20, 54) + 8
= 1080 + 8
= 1088.
answer :E
Answer: (E) 1088
Question: If p and y are positive integers such that p > y > 1, what is the remainder when 92p × 5p+y + 11y × 6py is divided by 10?
(A) A.0
(B) B.1
(C) C.3
(D) D.4
(E) E.5
Rationale: 92p × 5p+y + 11y × 6py--1=B
Answer: (B) B.1
Question: What is the area of a circle with the circumference of 88cms?
(A) 618sq cms
(B) 516sq cms
(C) 600sq cms
(D) 615sq cms
(E) None of these
Rationale: circum=2*pi*r
88=2*pi*r
r=44/pi
area of circle= pi * R2
a=pi*(44/pi)2
a=616
ANSWER:E
Answer: (E) None of these
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 700 m?
(A) 148.75 m
(B) 127.5 m.
(C) 122.2 m
(D) 222.9 m
(E) 12289 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800
= 6300/8
= 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 700 m, the number of meters by which A beats C = (700 * 212.5)/1000
= 148.75 m.
Answer:A
Answer: (A) 148.75 m
Question: If the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 5, what is the ratio of apples to cucumbers?
(A) 4:15
(B) 1:3
(C) 2:5
(D) 4:5
(E) 7:6
Rationale: Apples : Bananas = 4:3
Bananas : Cucumbers = 1:5 = 3:15
So if I have Bananas, I'd have 4 apples and 15 cucumbers
Apples : Cucumbers = 4:15
Answer: A
Answer: (A) 4:15
Question: A 70 kg metal bar made of alloy of tin and silver lost 7 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?
(A) 1/4
(B) 2/5
(C) 1/2
(D) 3/5
(E) 2/3
Rationale: you can simply use this formula to avoid confusion:
w1/w2 = (A2 - Aavg)/(Avg - A1)
Here is how you will find the values of A1 an A2.
We have an overall loss (average loss). The average loss is 7 kg when 70 kg alloy is immersed.
This is a loss of (7/70)*100 = 10%.
This is Aavg
The loss of tin is 1.375 kg for every 10 kg.
This means it loses (1.375/10)*100 = 13.75% of its weight in water.
This is A1.
The loss of silver is .375 kg for every 5 kg.
This means it loses (.375/5)* 100 = 7.5% of its weight in water.
This is A2.
Weight of Tin/Weight of Silver = (Silver's loss - Avg loss)/(Avg loss - Tin's loss)
X/Y = (7.5 - 10)/(10 - 13.75) = 2/3
E
Answer: (E) 2/3
Question: The ratio of scores of two football teams is 3 to 4. If each of the team had scores 5 more, what is the ratio of these two new scores ?
(A) 3/4
(B) 8/9
(C) 18/19
(D) 23/24
(E) It cannot be determined from the information given
Rationale: 3/4 = 3x/4x
we need to find out (3x+5)/(4x+5) off course we cannot solve this to arrive at any rational number hence E.
Answer: (E) It cannot be determined from the information given
Question: The average of 11 results is 42, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?
(A) 145
(B) 146
(C) 147
(D) 148
(E) 149
Rationale: 1 to 11 = 11 * 42= 462
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 – 462 = 147
ANSWER:C
Answer: (C) 147
Question: There is a 30 % chance of rain and a 70% chance of shine. If it rains there is a 50% chance that Bob will cancel his picnic but if the sun is shining he will definitely have his picnic. What is the chance that Bob will have his picnic?
(A) 70 %
(B) 75 %
(C) 80 %
(D) 85 %
(E) 90 %
Rationale: Chance of no picnic+chance of picnic= 100% ... (i)
Chance of picnic=100%-Chance of no picnic ... (ii)
Chance of no picnic= 50% of 30%= 15%
Therefore, According to (ii), Chance of picnic= 100%-15%= 85%.
Answer D
Answer: (D) 85 %
Question: CP of 3 buffaloes are $30,000. By selling 1 at a loss of 15% and other at a profit of 19%, he foundthat SP of both buffaloes is the same. Find the CP of each?
(A) $10,500
(B) $11,500
(C) $11,600
(D) $12,100
(E) $12,500
Rationale: Let the C.P of 1st buffalo = x
∴C.P of 2nd buffalo = 30,000 - x
S.P of 1st buffalo = ( 100 - loss% )
------------------- x C.P
100
S.P = 100 - 15x
-----------= 85x/ 100
100
S.P of 2nd buffalo = ( 100 - Profit%)
--------------------- x C.P
100
S.P = (100 + 19)(30,000- x) 119(30,000 -x)
-------------------- = ----------------
100 100
S.P of 1st buffalo = S.P of 2nd buffalo
85x/ 100 = 119 ( 30,000 - x)/ 100
⇒ 85x = 119(30,000 - x)
⇒ 85x = 3,570,000 - 119x
⇒ 85x + 119 x = 3,570,000
⇒ 204x = 3,570,000
⇒ x = 3,570,000 / 204
⇒ x = $17,500
C.P of 1st buffalo = $17,500
C.P of 2nd buffalo = 30,000 - 17,500 = $12,500
E
Answer: (E) $12,500
Question: The present ages of Lewis and Brown are in the ratio 1:2. Three years from now, the ages will be in the ratio 3:5. Find the present age of Lewis.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: l:b=1:2 & (l+3):(b+3)=3:5
then 2l=b & 5l+15=3b+9
by solving above we get
l=6
ANSWER:D
Answer: (D) 6
Question: Today is John's birthday. Three years from today he will be twice as old as he was 14 years ago. How old is John today ?
(A) 29 years
(B) 26 years
(C) 28 years
(D) 31 years
(E) 34 years
Rationale: let John's age=xx+3=2(x-14)x=31ANSWER:D
Answer: (D) 31 years
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 80/8
(B) 80/7
(C) 80/5
(D) 80/3
(E) 80/1
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
Answer: B
Answer: (B) 80/7
Question: A 16% stock yielding 14% is quoted at:
(A) s. 83.33
(B) s. 110
(C) s. 114
(D) s. 120
(E) s. 140
Rationale: Income of Rs 14 on investment of Rs 100
Income of Rs 16 on investment of ?
= (16*100)/14=114
ANSWER:C
Answer: (C) s. 114
Question: If 15% of a class averages 100% on a test, 50% of the class averages 78% on the test, and the remainder of the class averages 63% on the test, what is the overall class average? (Round final answer to the nearest percent).
(A) 76%
(B) 77%
(C) 78%
(D) 79%
(E) 80%
Rationale: This question is a Weighted Average question with a series of dependent variables.
The remaining portion of the class represents 100% - 15% - 50% = 35% of the class
Converting the portions of the class population to decimal weights, we find:
Class Average = 0.15x100 + 0.50x78 + 0.35x63 = 76.05
The class average (rounded) is 76%
Final Answer
A) 76%
Answer: (A) 76%
Question: 7 carpet-weavers can weave 7 carpets in 7 days. At the same rate, how many carpets would be woven by 14 carpet-weavers in 14 days?
(A) 14
(B) 28
(C) 21
(D) 35
(E) None of these
Rationale: Explanation :
Solution: Let the required number of carpets be x.
More weavers, more carpets (Direct proportion)
more days, more carpets (Direct proportion)
weavers 7 :14
} : : 7 : x
days 7 : 14
.'. 7*7*x = 14*14*7 <=> x = 14*14*7/7*7 = 28.
Answer : B
Answer: (B) 28
Question: The average of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 14 students?
(A) 16 years
(B) 76 years
(C) 14 years
(D) 19 years
(E) 15 years
Rationale: Sum of the ages of 14 students
= (16 * 35) - (14 * 21) = 560 - 294 = 266
Required average = (266/14) = 19 years.
Answer: D
Answer: (D) 19 years
Question: A train , having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
(A) 4 sec
(B) 2 sec
(C) 6 sec
(D) 8 sec
(E) 7 sec
Rationale: Distance = 110 m
Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 110/(110/6) = 6 s
Answer is C.
Answer: (C) 6 sec
Question: In what time a sum of money double itself at 7% per annum simple interest?
(A) 33 1/8%
(B) 33 1/3%
(C) 14 2/7%
(D) 33 4/3%
(E) 73 1/3%
Rationale: P = (P*7*R)/100
R = 14 2/7%
Answer:C
Answer: (C) 14 2/7%
Question: A cycle is bought for Rs.450 and sold for Rs.520, find the gain percent?
(A) 18
(B) 14
(C) 20
(D) 15
(E) 15.55
Rationale: 450 ---- 70
100 ---- ? => 15.55%
Answer: E
Answer: (E) 15.55
Question: Find the ratio in which rice at Rs.7.20 a kg be mixed with rice at Rs.5.60 a kg to produce a mixture worth Rs.6.30 a kg?
(A) 1 : 3
(B) 2 : 3
(C) 3 : 4
(D) 7 : 9
(E) None of these
Rationale: Solution
Required ratio = 70 : 90 = 7 : 9
Answer D
Answer: (D) 7 : 9
Question: If x is 20 percent greater than 88, then x =
(A) 68
(B) 70.4
(C) 86
(D) 105.6
(E) 108
Rationale: X is 20% greater than 88 means X is 1.2 times 88 (in other words 88 + 20/100 * 88 = 1.2 * 88)
Therefore, X = 1.2 * 88 = 105.6
ANSWER:D
Answer: (D) 105.6
Question: A man is 25 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is
(A) 21
(B) 22
(C) 20
(D) 18
(E) 23
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 25) years
=> (x + 25) + 2 = 2(x + 2)
=> x + 27 = 2x + 4
So, x = 23. Answer: E
Answer: (E) 23
Question: There are 300 seniors at Morse High School, and 40% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 20% of all the students at Morse have cars, how many students are in the three lower grades?
(A) 600
(B) 900
(C) 1200
(D) 1350
(E) 1500
Rationale: Let x be the number of students in the lower three grades.
0.1x + 120 = 0.2(x+300)
0.1x = 60
x = 600
The answer is A.
Answer: (A) 600
Question: How many questions should I solve the next hour to increase my average to 15 questions, if my average for last 2 hours has been 12 questions per hour.
(A) 8
(B) 10
(C) 12
(D) 18
(E) 21
Rationale: Answer:	Solution
Average of 3 days will be 15
âˆ´ Required questions = (3x15)-(2x12)
= 45-24
= 21.
Answer E
Answer: (E) 21
Question: Two digits in brother's age are the same as the digit in the sister's age, but in reverse order. In twenty nine years brother will be twice as old as sister will be then. what is the difference in their current age ?
(A) 34
(B) 50
(C) 32
(D) 28
(E) 45
Rationale: brother's age= 10x+y so sister's age= 10y+x..
after 29 years , 10x+y+29=2*(10y+x+29)....
so 29+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=6... so ages are 61 and 16 and ans as found correctly by u is E..45
Answer: (E) 45
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 5 boys when a boy gets any no. of prizes?
(A) 55
(B) 58
(C) 25
(D) 65
(E) 70
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (5x5) ways = 52 ways = 25 ways Or nr ways = 52 ways = 25 ways
Answer: (C) 25
Question: When positive integer N is divided by positive integer J, the remainder is 28. If N/J = 154.04, what is value of J?
(A) 400
(B) 350
(C) 700
(D) 750
(E) 800
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 154.04
Here 154 is the quotient.
Given that Remainder = 28
So, 154.04 = 154 + 28/J
So, J = 700
Answer: C
Answer: (C) 700
Question: A man recites the alphabet N times. What is the equation for the amount of every odd letter he said?
(A) 25/2*N
(B) 13N
(C) 27/2*N
(D) 26N
(E) 11N
Rationale: 13N is th Answer A
Answer: (A) 25/2*N
Question: The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10,
respectively. Due to a dramatic increase in the surrounding temperature, the composition of the
compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the
changed compound, if the total weight is 116 lbs, how much does substance x weigh?
(A) 48
(B) 36
(C) 24
(D) 12
(E) 10
Rationale: x:y=4:6
if the ratio is halevd then x:y=2:6
The old ratio of x to z was 4:10. If this ratio is tripled, then the new ratio of x to z is 12:10.
x:y=2:6=12:36 ( multiplied the ration with 6/6 to have a common co eff x in both the rations x:y and x:z)
so x:y:z= 12:36:10
and we know x + y + z = 116 lbs
from the ratio of x ,y and z we have x=12k y=36k z=10K
put it in the equation we have 12k+36k+10k=116
k=2
Hence x=12(2)=24
Ans C
Answer: (C) 24
Question: Albert buys 4 horses and 9 cows for Rs. 13,400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is?
(A) 1299
(B) 2788
(C) 2000
(D) 2981
(E) 2881
Rationale: Explanation:
Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y.
Then, 4x + 9y = 13400 -- (i)
And, 10% of 4x + 20% of 9y = 1880
2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)
Solving (i) and (ii), we get : x = 2000 and y = 600.
Cost price of each horse = Rs. 2000.
Answer: C
Answer: (C) 2000
Question: A jar contains a mixture of two liquids Acid( nitric acid) and Base(ammonium chloride) in the ratio 4 : 1. When 10 litres of the mixture is taken out and 10 litres of liquid Base is poured into the jar, the ratio becomes 2 : 3. How many litres of liquid Acid was contained in the jar?
(A) 14 lts
(B) 18 lts
(C) 20 lts
(D) 16 lts
(E) 26 lts
Rationale: %age of liquid Base in the original mixture
=1/5 x 100 = 20%
In the final mixture % of the liquid Base
= 3/5 x 100 = 60%
Now using the rule of allegation
Hence reduced quantity of the first mixture and the quantity of mixture B which is to be added are the same.
Total mixture = 10 + 10 = 20 liters and quantity of liquid A = 20/5 x 4 = 16 lts
ANSWER:D
Answer: (D) 16 lts
Question: On the Richter scale, which measures the total amount of energy released during an earthquake, a reading of x-1 indicates one-tenth the released energy as is indicated by a reading of x. On that scale, the frequency corresponding to a reading of 5 is how many times as great as the frequency corresponding to a reading of 3?
(A) 100
(B) 200
(C) 10^4
(D) 10^5
(E) 10^6
Rationale: If Richter scale reading goes from X-1 to X it will be 10
if Richter scale reading goes from 3 to 4 it will be 10
if Richter scale reading goes from 4 to 5 it will be 10
so it will from 3 to 5 i.e 4,5 = 10*10 = 10^2
Answer is A
Answer: (A) 100
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B at 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?
(A) 2387
(B) 267
(C) 120
(D) 277
(E) 271
Rationale: Let speed of the car be x km/hr.
Then, speed of the train = 150/100 x = 3/2 x km/hr.
75/x - 75/(3/2 x) = 125/(10 * 60)
75/x - 50/x = 5/24 = 120 km/hr.
Answer: C
Answer: (C) 120
Question: The difference between a two-digit number and the number obtained by interchanging the digit is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1:2?
(A) 8
(B) 15
(C) 14
(D) 12
(E) 10
Rationale: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let the ten's and unit's digits be 2x and x respectively.
Then, (10 * 2x + x) - (10x + 2x) = 36
9x = 36
x = 4
Required difference = (2x + x) - (2x - x) = 2x = 8.
ANSWER A
Answer: (A) 8
Question: Among 260 viewers interviewed who watch at least one of the three TV channels namely A, BC. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?
(A) 185
(B) 180
(C) 175
(D) 190
(E) 195
Rationale: 260 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)
260 = n(Exactly 1 channel) + 50 + n(Exactly 3 channels)
Let's find the value of n(Exactly 3 channels) = x
260 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.
260 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x
260 = 116 + 127 + 107 - 50 - 2x
x = 20
260 = n(Exactly 1 channel) + 50 + 20
n(Exactly 1 channel) = 190
Answer (D)
Answer: (D) 190