euclaise/mathqa_programs huggingface dataset:
Problem: a person crosses a 1800 m long street in 12 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 4.5 , c ) 4.8 , d ) 5.4 , e ) 9
Rationale: "speed = 1800 / ( 12 x 60 ) m / sec = 2.5 m / sec . converting m / sec to km / hr = 2.5 x ( 18 / 5 ) km / hr = 9 km / hr . answer : e"
Answer: e
Python program:
a = 1800 / 1000
b = 12 * const_60
c = b / 3600
d = a / c
Problem: calculate the amount that an investor needs to be invest to earn $ 1023 in interest in 24 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 12 % compounded semi - annually ?
Options: a ) 3980 , b ) 3600 , c ) 3700 , d ) 3800 , e ) 3900
Rationale: "the approach is substitution , our interest requirement is $ 1023 after 24 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields $ 1023 in 24 months 3900 yielded $ 1023 using the formula a = p ( 1 + r / n ) nt hence answer is e"
Answer: e
Python program:
a = 100 * 1023
b = a / 12
Problem: a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates c apply to what fraction of a week ?
Options: a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10
Rationale: "number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates c / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c"
Answer: c
Python program:
a = 24 / 2
b = 2 + 3 
c = a * b
d = 24 * 2
e = c + d 
f = 3 + 4 
g = 24 * f
h = e / g
Problem: a person can row at 9 kmph and still water . he takes 4 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 33 , b ) 77 , c ) 26 , d ) 28 , e ) 20
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 4.5 = > x / 10 + x / 8 = 9 / 2 = > ( 4 x + 5 x ) / 40 = 9 / 2 = > x = 20 km . answer : e"
Answer: e
Python program:
a = 9 - 1
b = 9 + 1 
c = a * b
d = c * 4
e = 9 + 1 
f = 9 - 1
g = e + f 
h = d / g
Problem: the distance from steve ' s house to work is 35 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 17.5
Rationale: time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 35 km = > speed = 17.5 kmph e
Answer: e
Python program:
a = 35 / 2
b = 35 + a 
c = b / 6
d = c * 2
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the 4 walls of the room at rs . 3 per square feet if there is one door of dimensions 6 feet * 3 feet and 3 windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4528 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 2718
Rationale: area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 3 = rs . 2718 answer : e
Answer: e
Python program:
a = 25 * 12
b = 15 * 12
c = a + b 
d = c * 2
e = 4 * 3
f = 3 * e
g = 6 * 3
h = f + g 
i = d - h
j = i * 3
Problem: the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively , is :
Options: a ) 123 , b ) 127 , c ) 235 , d ) 305 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1657 - 6 ) and ( 2037 - 5 ) = h . c . f . of 1651 and 2032 = 127 . answer : b"
Answer: b
Python program:
a = 2037 - 5
b = 1657 - 6
c = math.gcd(a, b)
Problem: in an examination , 300 students appeared . out of these students ; 28 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
Options: a ) 33 , b ) 37 , c ) 54 , d ) 99 , e ) 01
Rationale: "the number of students with first division = 28 % of 300 = 28 / 100 × 300 = 8400 / 100 = 84 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 84 + 162 ) = 54 answer : c"
Answer: c
Python program:
a = 28 + 54 
b = 100 - a
c = 300 * b
d = c / 100
Problem: the average of first 13 even numbers is ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "sum of 13 even numbers = 13 * 14 = 110 average = 182 / 13 = 14 answer : e"
Answer: e
Python program:
a = 13 + 1
Problem: a 250 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ?
Options: a ) 41.1 sec , b ) 20.2 sec , c ) 31.8 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 250 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 770 m time = distance / speed = 770 x 18 / ( 5 x 55 ) = 50.4 sec ans is : d"
Answer: d
Python program:
a = 250 + 520 
b = 55 * const_0_2778
c = a / b
Problem: what is 15 percent of 54 ?
Options: a ) 7.3 , b ) 8.1 , c ) 9.5 , d ) 10.2 , e ) 11.6
Rationale: "( 15 / 100 ) * 54 = 8.1 the answer is b ."
Answer: b
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 15 * n
p = o / 100
Problem: a sum of money at simple interest amount to rs 720 after 2 years and to rs 1020 after a further period of 5 years . the sum is :
Options: a ) 600 , b ) 450 , c ) 650 , d ) 500 , e ) 550
Rationale: simple interest for 5 year = rs . ( 1020 - 720 ) = rs . 300 . simple interest for 2 year = rs . ( 300 / 5 × 2 ) = rs . 120 . principal = rs . ( 720 - 120 ) = rs . 600 . answer : a
Answer: a
Python program:
a = 1020 - 720
b = a * 2
c = b / 5
d = 720 - c
Problem: an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 2 / 3 % , then the amount invested in each share was ?
Options: a ) 23777 , b ) 35000 , c ) 29977 , d ) 26777 , e ) 19871
Rationale: let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 29 / 3 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) / 100 = 29000 / 3 = 9700 ( 9 x + 1100000 - 11 x ) = 970000 x = 65000 sum invested at 9 % = rs . 65000 sum invested at 11 % = rs . ( 100000 - 65000 ) = rs . 35000 . answer : b
Answer: b
Python program:
a = 11 / 100
b = a * 100000
c = 2 / 3
d = 9 + c 
e = d / 100
f = e * 100000
g = b - f
h = 11 / 100
i = 9 / 100
j = h - i
k = g / j
l = 100000 - k
Problem: a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 100 more . what was the sum ?
Options: a ) s . 350 , b ) s . 700 , c ) s . 200 , d ) s . 600 , e ) s . 500
Rationale: "at 5 % more rate , the increase in s . i for 10 years = rs . 100 ( given ) so , at 5 % more rate , the increase in si for 1 year = 100 / 10 = rs . 10 / - i . e . rs . 10 is 5 % of the invested sum so , 1 % of the invested sum = 10 / 5 therefore , the invested sum = 10 × 100 / 5 = rs . 200 answer : c"
Answer: c
Python program:
a = 5 / 100
b = a * 10
c = 100 / b
Problem: a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 6,000 meters of fabric ?
Options: a ) $ 9,300 , b ) $ 10,400 , c ) $ 11,500 , d ) $ 12,600 , e ) $ 13,700
Rationale: "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 2500 = $ 4650 the total price is $ 4000 + $ 2850 + $ 4650 = $ 11,500 the answer is c ."
Answer: c
Python program:
a = 2 * 3
b = a * 100
Problem: there are 6 red balls and 4 blue balls in a jar . if 3 balls are selected from the jar , what is the probability that all 3 balls selected are blue balls ?
Options: a ) 1 / 18 , b ) 1 / 24 , c ) 1 / 30 , d ) 1 / 36 , e ) 1 / 48
Rationale: the number of ways of choosing 3 balls from the jar is 10 c 3 = 120 . the number of ways of choosing 3 blue balls is 4 c 3 = 4 . p ( 3 blue balls ) = 4 / 120 = 1 / 30 . the answer is c .
Answer: c
Python program:
a = math.comb(4, 3)
b = 6 + 4 
c = math.comb(b, 3)
d = a / c
Problem: in plutarch enterprises , 70 % of the employees are marketers , 10 % are engineers , and the rest are managers . marketers make an average salary of $ 50,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 370,000 , e ) $ 320,000
Rationale: for sake of ease , let ' s say there are 10 employees : 7 marketers , 1 engineers , and 2 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 50,000 ) and the engineers ( $ 80,000 ) > > > $ 800,000 - $ 350,000 - $ 80,000 = $ 370,000 . the correct answer is d .
Answer: d
Python program:
a = 70 + 10 
b = a * 1000
c = b * 100
d = 70 + 10 
e = d * 1000
f = 10 * e
g = c - f
h = 10 / 2
i = h * 10
j = i * 1000
k = j * 70
l = g - k
m = l / 10
Problem: working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel eight times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 8 and w = 8 s then we have 1 / ( 8 * s ) + 1 / s = 1 / 8 < = > 9 / ( 8 * s ) = 1 / 8 < = > s = 9 ans : d
Answer: d
Python program:
a = 2 * 4
b = 1/(a)
c = b + 1 
d = c * 3
e = 2 * 4
f = d * e
Problem: a boat running up stram takes 6 hours to cover a certain distance , while it takes 7 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ?
Options: a ) 2 : 3 , b ) 5 : 6 , c ) 4 : 5 , d ) 13 : 1 , e ) 8 : 1
Rationale: "explanation : let speed of boat is x km / h and speed stream is y km / hr 6 ( x + y ) = 7 ( x - y ) 6 x + 6 y = 7 x - 7 y 13 y = x 13 y = x x / y = 13 / 1 13 : 1 answer : option d"
Answer: d
Python program:
a = 7 - 6
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.6 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.6 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 32 hours . total hours = 72 then the fraction would be 32 / 72 = 4 / 9 . therefore answer e
Answer: e
Python program:
a = 3 + 2 
b = a / 10
Problem: a car traveled 75 % of the way from town a to town b at an average speed of 50 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 60 miles per hour . what is s ?
Options: a ) 150 , b ) 200 , c ) 250 , d ) 300 , e ) 237.5
Rationale: "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 50 = 1.5 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 60 = 1.5 + t » 100 / 60 = 1.5 + t » 2.5 = 1.5 + t » t = 0.1667 back to 2 nd part of the trip formula : 25 / s = 0.1667 » s = 150 ans a"
Answer: a
Python program:
a = 60 + 50 
b = a - 75
c = 60 + 50 
d = c / 60
e = 75 / 50
f = d - e
g = b / f
Problem: when positive integer n is divided by positive integer j , the remainder is 12 . if n / j = 134.02 , what is value of j ?
Options: a ) 300 , b ) 600 , c ) 500 , d ) 112 , e ) 620
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.02 , the decimal part of the decimal quotient , must equal the remainder , 12 , divided by the divisor j . 0.02 = 12 / j 0.02 * j = 12 j = 12 / 0.02 = 1200 / 2 = 600 / 1 = 600 so j = 600 , answer = b ."
Answer: b
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 134 - 2
e = 12 / d
Problem: joshua and jose work at an auto repair center with 5 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 21 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "two methods 1 ) probability of chosing josh first = 1 / 7 probability of chosing jose second = 1 / 6 total = 1 / 42 probability of chosing jose first = 1 / 7 probability of chosing josh second = 1 / 6 total = 1 / 42 final = 1 / 42 + 1 / 42 = 1 / 21 a"
Answer: a
Python program:
a = math.factorial(6)
b = math.factorial(2)
c = math.factorial(5)
d = b * c
e = a / d
f = math.factorial(6)
g = e / f
Problem: in the coordinate plane , points ( x , 2 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y =
Options: a ) 4.5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 2 ) = ( 4 , 2 ) and ( 10 , y ) = ( 10,5 ) - - > 4 + 5 = 2 + 5 = 9 . answer : c ."
Answer: c
Python program:
a = 10 * 4
b = 2 / 2
c = a * b
Problem: the average score of a cricketer in 2 matches is 20 and in other 3 matches is 30 . then find the average score in all the 5 matches ?
Options: a ) 26 , b ) 27 , c ) 30 , d ) 35 , e ) 42
Rationale: "average in 5 matches = ( 2 * 20 + 3 * 30 ) / 2 + 3 = 40 + 90 / 5 = 130 / 5 = 26 answer is a"
Answer: a
Python program:
a = 2 * 20
b = 3 * 30
c = a + b 
d = c / 5
Problem: 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 10 mat - weavers in 10 days ?
Options: a ) 25 , b ) 19 , c ) 39 , d ) 61 , e ) 16
Rationale: "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 10 : : 4 : x days 4 : 10 4 * 4 * x = 10 * 10 * 4 x = ( 10 * 10 * 4 ) / ( 4 x 4 ) x = 25 . answer is a ."
Answer: a
Python program:
a = 10 / 4
b = 4 * a
c = 10 / 4
d = b * c
Problem: rahul played weel in this season . his current batting averagge is 51 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: "51 x + 78 = 54 ( x + 1 ) = > 3 x = 24 = > x = 8 answer : a"
Answer: a
Python program:
a = 78 - 54
b = 54 - 51
c = a / b
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 14 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 112 % , e ) 138 %
Rationale: "0,112 r = x / 100 * 0.1 r answer d"
Answer: d
Python program:
a = 20 / 100
b = 1 - a
c = 14 / 100
d = b * c
e = 10 / 100
f = d / e
g = f * 100
Problem: a garrison of 400 men had a provision for 31 days . after 25 days 320 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 65 days , b ) 30 days , c ) 10 days , d ) 16 days , e ) 18 days
Rationale: "400 - - - 31 400 - - - 6 80 - - - ? 400 * 6 = 80 * x = > x = 30 days . answer : b"
Answer: b
Python program:
a = 31 - 25
b = a * 400
c = b / 320
Problem: a jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . the train is running at 45 kmph in the same direction . how much time does it take for the train to pass the jogger ?
Options: a ) 46 , b ) 36 , c ) 18 , d ) 22 , e ) 23
Rationale: explanation : distance to be covered = 240 + 120 = 360 m relative speed = 36 km / hr = 36 × 10 / 36 = 10 m / s time = distance / speed = 360 / 10 = 36 seconds answer : option b
Answer: b
Python program:
a = 240 + 120 
b = 45 - 9
c = b * 1000
d = c / 3600
e = a / d
Problem: the dimensions of a field are 10 m by 10 m . a pit 5 m long , 5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ?
Options: a ) 2 m , b ) 2.5 m , c ) 1.5 m , d ) 1.25 m , e ) 1 m
Rationale: "the volume of the earth removed is 5 * 5 * 3 = 75 m ^ 3 . the remaining area of the field is 10 * 10 - 5 * 5 = 75 m ^ 2 . 75 m ^ 3 of the earth evenly spread over the area of 75 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 75 / 75 = 1 m . answer : e"
Answer: e
Python program:
a = 10 * 5
b = rectangle_area - (
c = a / b
Problem: suganya and suriya are partners in a business . suganya invests rs . 32,000 for 8 months and suriya invests rs . 28,000 for 10 months . out of a profit of rs . 30,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 912.54 , d ) rs . 18,942 , e ) none
Rationale: "solution ratio of their shares = ( 32000 ã — 8 ) : ( 28000 ã — 10 ) = 32 : 35 . suganya ' s share = rs . ( 31570 ã — 2 / 67 ) = rs . 912.54 . answer c"
Answer: c
Python program:
a = const_0_25 * 100
b = a * 10
Problem: a number when divided by a divisor leaves a remainder of 24 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 13 , b ) 59 , c ) 35 , d ) 37 , e ) 12
Rationale: "explanatory answer decoding ` ` a number when divided by a divisor leaves a remainder of 24 ' ' let the original number be ' a ' . let the divisor be ' d ' . let the quotient of dividing ' a ' by ' d ' be ' x ' . therefore , we can write the division as a / d = x and the remainder is 24 . i . e . , a = dx + 24 decoding ` ` when twice the original number is divided by the same divisor , the remainder is 11 ' ' twice the original number is divided by d means 2 a is divided by d . we know that a = dx + 24 . therefore , 2 a = 2 ( dx + 48 ) or 2 a = 2 dx + 48 when ( 2 dx + 48 ) is divided by ' d ' the remainder is 11 . 2 dx is divisible by ' d ' and will therefore , not leave a remainder . the remainder of 11 would be the remainder of dividing 48 by d . the question is ` ` what number will leave a remainder of 11 when it divides 48 ? ' ' when 37 divides 48 , the remainder is 11 . hence , the divisor is 37 . choice d"
Answer: d
Python program:
a = 24 + 11
Problem: an uneducated retailer marks all his goods at 65 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ?
Options: a ) 12.50 % , b ) 13.50 % , c ) 14 % , d ) 23.75 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 165 . s . p . = 75 % of rs . 165 = rs . 123.75 . ∴ gain % = 23.75 % . answer d"
Answer: d
Python program:
a = 65 / 100
b = 1 + a 
c = 65 / 100
d = 1 + c 
e = 25 / 100
f = d * e
g = b - f
h = g - 1
i = h * 100
Problem: a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 126 km downstream .
Options: a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 126 / 21 = 6 hours option c
Answer: c
Python program:
a = 16 + 5 
b = 126 / a
Problem: if 7 a = 2 b = 15 , then 42 ab =
Options: a ) 75 , b ) 125 , c ) 675 , d ) 1100 , e ) 1250
Rationale: "7 a * 2 b = 15 * 15 = 225 14 ab = 225 i . e . 42 ab = 675 answer : option c"
Answer: c
Python program:
a = 15 / 7
b = 15 / 2
c = a * b
d = 42 * c
Problem: 10 friends went to a hotel and decided to pay the bill amount equally . but 9 of them could pay rs . 50 each as a result 10 th has to pay rs . 180 extra than his share . find the amount paid by him .
Options: a ) 130 , b ) 140 , c ) 110 , d ) 120 , e ) none
Rationale: "explanation : average amount paid by 9 persons = rs . 50 increase in average due to rs . 50 paid extra by the 10 th men = rs . 180 / 9 = rs . 20 therefore , average expenditure of 10 friends = rs . 50 + rs . 20 = rs . 70 therefore , amount paid by the 10 th men = rs . 70 + rs . 50 = rs . 120 correct option : d"
Answer: d
Python program:
a = 50 * 9
b = a + 180 
c = b / 9
d = 180 + c
Problem: if 0.75 : x : : 5 : 7 , then x is equal to :
Options: a ) 1.05 , b ) 1.16 , c ) 1.2 , d ) 1.3 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 7 ) x = 5.25 / 5 = 1.05 answer : a"
Answer: a
Python program:
a = 0 * 75
b = a / 5
Problem: a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 7 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 67 / 90 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "i think a - 67 / 90 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 7 x so old = x , new = 6 x now 1 / 3 of x are occupied and 1 / 5 of 6 x are occupied which simplifies to ( 6 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 6 / 5 of x occupied in the new ward . add them up to get 23 / 15 of x there are 6 x beds in new tower so ratio is : ( 23 / 15 ) x / 6 x = 23 / 90 of x subtract that from 90 / 90 of x and you get the number of un - occupied beds to total capacity of new tower = 67 / 90 . a"
Answer: a
Python program:
a = 7 * 3
b = a + 1 
c = 1 / 3
d = 1 / 5
e = c * d
f = b * e
Problem: a man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes . his rowing speed in s ɵ ll water is
Options: a ) 4 kmph , b ) 5 kmph , c ) 6 kmph , d ) 7 kmph , e ) none of these
Rationale: explanation : rate upstream = ( 750 / 675 ) = 10 / 9 m / sec rate downstream ( 750 / 450 ) m / sec = 5 / 3 m / sec rate in still water = ( 1 / 2 ) * [ ( 10 / 9 ) + ( 5 / 3 ) ] m / sec . = 25 / 18 m / sec = ( 25 / 18 ) * ( 18 / 5 ) kmph = 5 kmph answer : b
Answer: b
Python program:
a = 7 * const_60
b = 1 * const_60
c = b / 2
d = a + c 
e = 750 / d
f = 750 / 675
g = e + f 
h = 1 / 2
i = g * h
j = const_3_6 * i