euclaise/mathqa_programs huggingface dataset:
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price r per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."
Answer: d
Python program:
a = 1 + 1 
b = a * 0
c = 1 + 2 
d = b / c
Problem: two numbers are in the ratio of 2 : 3 . if 4 is added in both numbers the ratio becomes 5 : 7 . find the difference between numbers .
Options: a ) 8 , b ) 6 , c ) 4 , d ) 2 , e ) 10
Rationale: we ' re told that two numbers are in the ratio of 2 : 3 . thus , the two numbers could be . . . 2 and 3 4 and 6 6 and 9 8 and 12 10 and 15 etc . we ' re told that adding 4 to each number changes the ratio of the numbers to 5 : 7 . we ' re asked for the difference between the original numbers . since adding 4 makes the first number a multiple of 5 , this limits the possibilities . . . . 2 + 4 = 6 not possible 4 + 4 = 8 not possible 6 + 4 = 10 this is possible . . . using this example , we would have . . . 6 and 9 , after adding 4 to each , becomes 10 and 13 . . . this is not a ratio of 5 to 7 though ( even though it ' s pretty close ) , so we have to keep looking . . . . the next value that becomes a multiple of 5 when you add 4 to it is . . . 16 . . . 16 + 4 = 20 with 16 and 24 , after adding 4 to each , we have 20 and 28 . this is a ratio of 5 to 7 , so we have our pair of original numbers . the difference between them is 8 . final answer : a
Answer: a
Python program:
a = 7 * 4
b = 5 * 4
c = a - b
d = c * 2
e = 3 / 2
f = d * e
g = 7 * 4
h = 5 * 4
i = g - h
j = i * 2
k = f - j
Problem: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6600 . find the actual price of the good .
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9649 , e ) s . 9980
Rationale: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6600 1 = 6600 / 68.4 100 = ( 6600 * 100 ) / 68.4 = rs . 9649 . answer : option d"
Answer: d
Python program:
a = 6600 * 100
b = 100 - 20
c = 100 - 20
d = c * 10
e = d / 100
f = b - e
g = 100 - 20
h = 100 - 20
i = h * 10
j = i / 100
k = g - j
l = k * 5
m = l / 100
n = f - m
o = a / n
Problem: in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 55 % , and the students on the make - up date had an average score of 95 % , what was the average score for the entire class ?
Options: a ) 60 % , b ) 65 % , c ) 67 % , d ) 70 % , e ) 75 %
Rationale: "70 % of the class scored 55 % and 30 % of the class scored 95 % . the difference between 55 % and 95 % is 40 % . the average will be 55 % + 0.3 ( 40 % ) = 67 % . the answer is c ."
Answer: c
Python program:
a = 70 * 55
b = 100 - 70
c = 95 * b
d = a + c 
e = d / 100
Problem: excluding stoppages , the speed of a bus is 64 kmph and including stoppages , it is 50 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 15.5 , b ) 12.3 , c ) 10.5 , d ) 10.12 , e ) 13.12
Rationale: "due to stoppages , it covers 14 km less . time taken to cover 14 km = ( ( 14 / 64 ) ã — 60 ) = 13.12 min . option ( e ) is correct"
Answer: e
Python program:
a = 64 - 50
b = a / 64
c = const_60 * b
Problem: a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 8 hours , b ) 10 hours , c ) 12 hours , d ) 24 hours , e ) none of the above
Rationale: "a ' s 1 hour ' s work = 1 / 4 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( b + c ) ' s 1 hour ' s work = 1 / 2 ( a + b + c ) ' s 1 hour ' s work = ( 1 / 4 + 1 / 3 ) = 7 / 12 b ' s 1 hour ' s work = ( 7 / 12 - 1 / 2 ) = 1 / 12 b alone will take 12 hours to do the work . answer = c"
Answer: c
Python program:
a = 1 / 3
b = 1 / 2
c = 1 / 4
d = b - c
e = a - d
f = 1 / e
Problem: the moon revolves around the earth at a speed of approximately 1.02 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 62.5 , d ) 3,600 , e ) 3,672
Rationale: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.02 * 3600 = 3672 kilometers per hour . option e is correct"
Answer: e
Python program:
a = 1 * 2
Problem: the ratio of football players , baseball players , soccer players , and basketball players in a school is 10 : 7 : 5 : 4 . how many athletes are in the school if 16 players are on the basketball team ?
Options: a ) 40 , b ) 92 , c ) 104 , d ) 208 , e ) 80
Rationale: the ratio is 10 football players : 7 baseball players : 5 soccer players : 4 basketball players . divide 16 by 4 to find 1 ` ` part ' ' of the ratio . 16 / 4 = 4 multiply 4 by 5 to find the number of soccer players . 4 * 5 = 20 multiply 4 by 7 to find the number of baseball players . 4 * 7 = 28 multiply 4 by 10 to find the number of football players . 4 * 10 = 40 . add them all up to find total athletes . 16 + 20 + 28 + 40 = 104 the answer is c .
Answer: c
Python program:
a = 5 * 16
b = a / 4
c = b + 16 
d = 7 * 16
e = d / 4
f = c + e 
g = 10 * 16
h = g / 4
i = f + h
Problem: 7386038 is divisible by
Options: a ) 3 , b ) 4 , c ) 9 , d ) 11 , e ) 13
Rationale: "explanation : the given number is 7386038 . the sum of the digits at even places is = 3 + 6 + 3 = 12 . the sum of the digits at odd places is = 7 + 8 + 0 + 8 = 23 . the difference is given by 23 - 12 = 11 answer : d"
Answer: d
Python program:
a = 1 + 4 
b = 7386038 / a
c = math.floor(b)
d = 1 + 4 
e = d ** 2
f = 7386038 / e
g = math.floor(f)
h = c + g
Problem: 40 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 299 , b ) 277 , c ) 800 , d ) 289 , e ) 271
Rationale: "( 40 / 100 ) * x – ( 20 / 100 ) * 650 = 190 2 / 5 x = 320 x = 800 answer : c"
Answer: c
Python program:
a = 650 * 20
b = a / 100
c = b + 190 
d = c * 100
e = d / 40
Problem: what is the sum of the digits of integer k , if k = ( 10 ^ 30 - 36 )
Options: a ) 251 , b ) 260 , c ) 263 , d ) 269 , e ) 262
Rationale: there are 31 digits in 10 ^ 30 when we subtract 36 from it , there will be 30 digits left . 10 ^ 30 can be written as 9999999 . . . . ( 30 times ) + 1 so , 10 ^ 30 - 36 = 9999999 . . . . ( 30 times ) + 1 - 36 = 9999999 . . . . ( 30 times ) - 35 consider the last 2 digits , 99 - 35 = 64 the last 2 digits will be 64 . and our number would be 99999 . . . . . . 99964 with 2 less 9 s after subtraction . number of 9 s left are 28 and the last two digits are 64 the sum of the digits will be ( 28 * 9 ) + 6 + 4 = 262 answer : - e
Answer: e
Python program:
a = 10 - 1
b = 30 - 2
c = a * b
d = c + 10
Problem: if a # b = ab – b + b ^ 2 , then 3 # 7 =
Options: a ) 2 , b ) 63 , c ) 15 , d ) 21 , e ) 35
Rationale: solution - simply substitute 3 and 7 in equation in the place of a and b respectively . 3 # 7 = 3 * 7 - 7 + 7 ^ 2 = 21 - 7 + 49 = 63 . ans b
Answer: b
Python program:
a = 3 * 7
b = a - 7
c = 7 ** 2
d = b + c
Problem: a train covers a distance of 12 km in 10 min . if it takes 4 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 20 , b ) 110 , c ) 120 , d ) 80 , e ) 60
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 4 = 80 m . answer : option d"
Answer: d
Python program:
a = 12 / 10
b = a - 4
c = 12 / b
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction w of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction w of n to the total would be 4 a / 24 a or 1 / 6 answer b"
Answer: b
Python program:
a = 1 * 1
b = 20 / 4
c = b + 21 
d = c / 4
e = d * 2
f = e - 4
g = f - 3
h = a / g
Problem: the average salary of 16 people in the shipping department at a certain firm is $ 20000 . the salary of 5 of the employees is $ 25000 each and the salary of 4 of the employees is $ 16000 each . what is the average salary of the remaining employees ?
Options: a ) $ 18,714 , b ) $ 18,500 , c ) $ 18,000 , d ) $ 15,850 , e ) $ 12,300
Rationale: total salary . . . 16 * 20 k = 320 k 5 emp @ 25 k = 125 k 4 emp @ 16 k = 64 k remaing 7 emp sal = 320 k - 125 k - 64 k = 131 k average = 131 k / 7 = 18714 ans : a
Answer: a
Python program:
a = 16000 - 20000
b = 4 * a
c = 25000 - 20000
d = 5 * c
e = b + d 
f = 5 + 4 
g = 16 - f
h = e / g
i = 20000 - h
j = i / 1000
Problem: jerry went to a shop and bought things worth rs . 40 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19 , b ) 19.7 , c ) 21.3 , d ) 31.5 , e ) 34.7
Rationale: "total cost of the items he purchased = rs . 40 given that out of this rs . 40 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 40 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 40 − 0.3 − x ) = 30 ⇒ ( 40 − 0.3 − x ) = 5 ⇒ x = 40 − 0.3 − 5 = 34.7 e )"
Answer: e
Python program:
a = 30 / 100
b = 100 / 6
c = a * b
d = 30 / 100
e = c + d 
f = 40 - e
Problem: a no . when divided by 142 gives a remainder 110 , what remainder will be obtainedby dividingthe same no . 14 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: 142 + 110 = 252 / 14 = 18 ( remainder ) c
Answer: c
Python program:
a = 142 + 110 
b = a / 14
Problem: two stations a and b are 110 km apart on a straight line . one train starts from a at 6 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 12 , e ) 15
Rationale: "suppose they meet x hours after 6 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 9 a . m . answer : c"
Answer: c
Python program:
a = 110 - 20
b = 25 + 20 
c = a / b
d = 8 + c
Problem: one pipe can fill a tank four times as fast as another pipe . if together the two pipes can fill the tank in 40 minutes , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 100 min , b ) 150 min , c ) 200 min , d ) 250 min , e ) 300 min
Rationale: "let the slower pipe alone fill the tank in x minutes then , faster pipe will fill it in x / 4 minutes 1 / x + 4 / x = 1 / 40 5 / x = 1 / 40 x = 200 min answer is c"
Answer: c
Python program:
a = 1 + 4 
b = a * 40
Problem: a scale 6 ft . 8 inches long is divided into 5 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 16 inches , d ) 97 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 5 parts = 80 / 5 = 16 inches answer : c"
Answer: c
Python program:
a = 6 * 12
b = a + 8 
c = b / 5
Problem: the area of rhombus is 150 cm square . the length of one of the its diagonals is 10 cm . the length of the other diagonal is :
Options: a ) 15 cm
b ) 20 cm
c ) 25 cm
d ) 30 cm
e ) none of these
Rationale: explanation : we know the product of diagonals is 1 / 2 * ( product of diagonals ) let one diagonal be d 1 and d 2 so as per question 1 / 2 ∗ d 1 ∗ d 2 = 150 1 / 2 ∗ 10 ∗ d 2 = 150 d 2 = 150 / 5 = 30 option d
Answer: d
Python program:
a = 150 * 2
b = a / 10
Problem: machine a can finish a job in 4 hours , machine в can finish the job in 3 hours , and machine с can finish the job in 6 hours . how many hours will it take for a , b , and с together to finish the job ?
Options: a ) 3 / 2 , b ) 4 / 3 , c ) 5 / 4 , d ) 6 / 5 , e ) 8 / 7
Rationale: "the combined rate is 1 / 4 + 1 / 3 + 1 / 6 = 9 / 12 of the job per hour . the time to complete the job is 12 / 9 = 4 / 3 hours . the answer is b ."
Answer: b
Python program:
a = 1/(4)
b = 1/(3)
c = a + b 
d = 1/(6)
e = c + d 
f = 1/(e)
Problem: if 10 litres of an oil of rs . 55 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 51.03 , c ) rs . 58.66 , d ) rs . 55.33 , e ) none of the above
Rationale: 55 * 10 = 550 66 * 5 = 330 880 / 15 = 58.66 answer : c
Answer: c
Python program:
a = 10 * 55
b = 5 * 66
c = a + b 
d = 10 + 5 
e = c / d
Problem: a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , a receives :
Options: a ) rs . 8400 , b ) rs . 11,900 , c ) rs . 13,600 , d ) rs . 14,700 , e ) none of these
Rationale: explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 35000 x 21 / 50 ) = rs . 14,700 . answer is d
Answer: d
Python program:
a = 10 * 5000
b = a - 5000
c = 4000 + 5000 
d = b - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 10 * 5000
i = g / h
j = 3 + 4 
k = j * 5000
l = i * k
m = l / 1000
n = math.floor(m)
o = n - 1
Problem: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 700 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) 1800
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 700 = 16200 exp in % = 100 - 10 = 90 % , 16200 = 90 % saving = 10 % = 16200 x 10 / 90 = rs . 1800 answer : e"
Answer: e
Python program:
a = 5000 + 1500 
b = a + 4500 
c = b + 2500 
d = c + 2000 
e = d + 700 
f = e * 100
g = 100 - 10
h = f / g
i = 5000 + 1500 
j = i + 4500 
k = j + 2500 
l = k + 2000 
m = l + 700 
n = h - m
Problem: if the radius of a circle decreased by 50 % its area is decreased by :
Options: a ) 75
b ) 79
c ) 72
d ) 70
e ) 80
Rationale: original area = π r ( power ) 2 new area = π ( r / 2 ) ( power ) 2 = ( π r ( power ) 2 ) / 4 reduction in area = [ ( π r ( power ) 2 - ( π r ( power ) 2 ) / 4 ] 2 = ( 3 π r ( power ) 2 ) / 4 reduction percent = ( ( 3 π r ( power ) 2 ) / 4 × 1 / ( π r ( power ) 2 × 100 ) % = 75 % answer is a .
Answer: a
Python program:
a = 50 / 100
b = a ** 2
c = b * 100
d = 100 - c
Problem: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction e of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?
Options: a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14
Rationale: if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus e = 11 / 14 of the remaining votes must be against . answer : a .
Answer: a
Python program:
a = 1 + 2 
b = 2 / a
c = 2 / 9
d = 2 / 9
e = 3 / 4
f = d * e
g = c - f
h = b - g
i = 9 - 2
j = i / 9
k = h / j
Problem: a is thrice as good a work man as b and together they finish a piece of work in 16 days . the number of days taken by b alone to finish the work is :
Options: a ) 64 days . , b ) 24 days . , c ) 52 days . , d ) 35 days . , e ) 28 days .
Rationale: "solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 3 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 16 divide 1 / 14 in the ratio 3 : 1 . ∴ b ’ s 1 day ’ s work = ( 1 / 16 x 1 / 4 ) = 1 / 64 hence , b alone can finish the work in 64 days . answer a"
Answer: a
Python program:
a = 3 + 1 
b = 16 / 3
c = a * b
Problem: if a large pizza has a radius that is 50 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 125 % , e ) 150 %
Rationale: "let the radius of medium pizza be r . then the radius of large pizza is 1.5 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.5 * r ) ^ 2 = 2.25 * pi * r ^ 2 , an increase of 125 % . the answer is d ."
Answer: d
Python program:
a = 50 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = d * 100
Problem: if it takes 10 kids 6 hours to wear out their teacher , how long would it take 15 kids ?
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) 1 hour
Rationale: 10 * 6 = 15 * x x = 4 answer : b
Answer: b
Python program:
a = 10 * 6
b = a / 15
Problem: the mass of 1 cubic meter of a substance is 500 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 0.1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "500 kg - 1 cubic meter ; 500,000 g - 1 cubic meter ; 500,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 500,000 = 10 / 5 = 2 cubic centimeters . answer : d ."
Answer: d
Python program:
a = 1 * 0
b = 500 * 1
c = a / b
Problem: john found that the average of 15 numbers is 40 . if 13 is added to each number then the mean of number is ?
Options: a ) 53 , b ) 45 , c ) 65 , d ) 78 , e ) 64
Rationale: "( x + x 1 + . . . x 14 ) / 15 = 40 53 option a"
Answer: a
Python program:
a = 40 + 13
Problem: a straight line in the xy - plane has y - intercept of 10 . on this line the x - coordinate of the point is 100 and y - coordinate is 1000 then what is the slope of the line ?
Options: a ) 2 , b ) 5.5 , c ) 6.5 , d ) 3.2 , e ) 9.9
Rationale: eq of line = y = mx + c c = 10 x = 100 y = 100 m + 10 , substitute y by 1000 as given in question . 1000 = 100 m + 10 , m = 9.9 . correct option is e
Answer: e
Python program:
a = 1000 - 10
b = a / 100
Problem: a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . what is the length of the bridge ( in metres ) ?
Options: a ) 1280 , b ) 1250 , c ) 1320 , d ) 1340 , e ) 1350
Rationale: speed = 5 km / hr time = 15 minutes = 1 / 4 hour length of the bridge = distance travelled by the man = speed × time = 5 × 1 / 4 km = 5 × ( 1 / 4 ) × 1000 metre = 1250 metre answer is b
Answer: b
Python program:
a = 5 * 1000
b = a / const_60
c = b * 15
Problem: a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 40 % , what should be the sale price of the mixed tea ?
Options: a ) 22.4 , b ) 22 , c ) 20 , d ) 19.2 , e ) none of these
Rationale: c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 40 ) / 100 × 16 = 22.4 answer a
Answer: a
Python program:
a = 80 * 15
b = 20 * 20
c = a + b 
d = 80 + 20 
e = c / d
f = e * 40
g = f / 100
h = 80 * 15
i = 20 * 20
j = h + i 
k = 80 + 20 
l = j / k
m = g + l
Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability z that the first ball picked up is odd numbered ?
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability z is 2 / 3 . d"
Answer: d
Python program:
a = 2 / 3
Problem: if the price of a book is first decreased by 30 % and then increased by 40 % , then the net change in the price will be :
Options: a ) 10 , b ) 388 , c ) 37 , d ) 29 , e ) 2
Rationale: "explanation : let the original price be rs . 100 . decreased by 30 % = 70 then increased 40 % on rs 70 = 70 + 28 = 98 net change in price = 100 - 98 = 2 answer : e"
Answer: e
Python program:
a = 100 * 30
b = a / 100
c = 100 - b
d = c / 100
e = 100 * 40
f = e / 100
g = 100 + f 
h = g / 100
i = d * h
j = i * 100
k = 100 - j
Problem: two pipes a and b can fill a cistern in 37 ½ min and 45 minutes respectively . both the pipes are opened . the cistern will be filled in just half an hour , if the pipe b is turned off after
Options: a ) 6 minutes , b ) 9 minutes , c ) 45 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: if pipe b is turned off after x mins , then ( 2 * 30 ) / 75 + x / 45 = 1 x / 45 = 1 - 60 / 75 = 1 / 5 x = 45 / 5 = 9 mins answer : b
Answer: b
Python program:
a = 2 + 3 
b = 45 / a
Problem: all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 158 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1264 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: "a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 158 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 158 = 3 k + 158 = > 2 k = 316 = > k = 158 the initial quantity of milk in a = 8 k = 8 * 158 = 1264 liters ."
Answer: a
Python program:
a = 1/(2)
b = 62 / 5
c = 1 - b
d = a - c
e = 158 / d
Problem: two spies agreed to meet at a gas station between noon and 1 pm , but they have both forgotten the arranged time . each arrives at a random time between noon and 1 pm and stays for 6 minutes unless the other is there before the 6 minutes are up . assuming all random times are equally likely , what is the probability that they will meet within the hour ( noon to 1 pm ) ?
Options: a ) 0.12 , b ) 0.15 , c ) 0.17 , d ) 0.19 , e ) 0.25
Rationale: the probability that they do not meet is represented by the total of the areas of the two outer triangles in the figure below , which is 0.81 . so the probability of a meeting is 1 - 0.81 = 0 . 19 . correct answer d
Answer: d
Python program:
a = 6 * 3
b = a + 1 
c = b / 100