euclaise/mathqa_programs huggingface dataset:
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 10 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 55 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 10 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 10 = 4 / 9 ( t - 10 ) 10 t = 990 - 440 = > t = 55 . answer : d"
Answer: d
Python program:
a = 6 / 5
b = a * 5
c = b - 4
d = 10 / c
e = 5 * d
f = 6 / 5
g = f * 5
h = g - 4
i = 10 / h
j = e + i 
k = j + 10
Problem: in a particular state , 70 % of the counties received some rain on monday , and 50 % of the counties received some rain on tuesday . no rain fell either day in 20 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "70 + 50 + 20 = 140 % the number is 40 % above 100 % because 40 % of the counties were counted twice . the answer is b ."
Answer: b
Python program:
a = 70 + 50 
b = 100 - 20
c = a - b
Problem: a train passes a platform in 16 seconds . the same train passes a man standing on the platform in 10 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 40 , b ) 50 , c ) 90 , d ) 30 , e ) 20
Rationale: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 10 = 150 m let the length of the platform = l time taken to cross the platform = ( 150 + l ) / 15 = > ( 150 + l ) / 15 = 16 = > 150 + l = 15 × 16 = 240 = > l = 240 - 150 = 90 meter answer is c"
Answer: c
Python program:
a = const_0_2778 * 54
b = 16 - 10
c = a * b
Problem: a certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 180 , e ) 315
Rationale: "1 of 7 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more thn one deparments . we can choose any of the 4 candidates for the math dep . , which gives as 4 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 4 * 45 = 180 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans d"
Answer: d
Python program:
a = 10 * 3
b = a * 4
Problem: sum of two numbers is 25 . first exceeds by 5 from the other . then the numbers will be ?
Options: a ) 20 , 5 , b ) 10 , 15 , c ) 15 , 10 , d ) 5 , 20 , e ) 12 , 13
Rationale: "explanation : x + y = 25 x - y = 5 x = 15 y = 10 answer : c"
Answer: c
Python program:
a = 5 / 2
b = 25 - a
c = b / 2
d = 25 - c
Problem: if 35 % of the 840 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 546 , b ) 550 , c ) 555 , d ) 532 , e ) 515
Rationale: "we know 35 % people study biology , therefore the no of people not studying = 100 - 35 = 65 % > therefore the people not studying biology out of a total 840 people are = 65 % of 840 > ( 65 / 100 ) * 840 = 546 people a"
Answer: a
Python program:
a = 840 / 100
b = 100 - 35
c = a * b
Problem: a train is 410 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 76 seconds , b ) 18 seconds , c ) 40 seconds , d ) 19 seconds , e ) 44 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 410 + 140 = 550 meter time = distance / speed = 550 * ( 2 / 25 ) = 44 seconds answer : e"
Answer: e
Python program:
a = 410 + 140 
b = 45 * 1000
c = b / 3600
d = a / c
Problem: if a is thrice as fast as b and together can do a work in 30 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 42 , c ) 28 , d ) 54 , e ) 40
Rationale: a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 30 = 3 + 1 / 3 x = 4 / 3 x = 1 / 30 x = 30 * 4 / 3 = 40 answer : e
Answer: e
Python program:
a = 30 * 4
b = 3 / a
c = 1/(b)
Problem: angelina walked 200 meters from her home to the grocery at a constant speed . she then walked 300 meters to the gym at double the speed . she spent 50 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 200 / x . . the speed to gym = 2 x . . so time taken = 300 / 2 x = 150 / x . . its given 200 / x - 150 / x = 50 . . 50 / x = 50 . . x = 1 m / secs . . so grocery to gym = 2 * 1 = 2 m / s . . . answer : a"
Answer: a
Python program:
a = 300 / 2
b = 200 - a
c = b / 50
d = c * 2
Problem: the sum of the ages of 5 children born at the intervals of 3 year each is 40 year . what is the age of the eldest child ?
Options: a ) 14 year , b ) 8 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 40 â ‡ ” 5 x = 10 â ‡ ” x = 2 . â ˆ ´ age of the youngest child = x + 12 = 2 + 12 = 14 years . answer a"
Answer: a
Python program:
a = 5 / 3
b = 40 / a
c = 5 - 1
d = c * 3
e = b - d
f = e / 3
Problem: how many positive integers less than 5,000 are evenly divisible by neither 17 nor 21 ?
Options: a ) 4,514 , b ) 4,480 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 17 5000 / 17 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 17 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 17 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4480 answer b ."
Answer: b
Python program:
a = 4 + 17 
b = a - 1
c = math.factorial(b)
d = math.factorial(17)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 2 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 40 , d ) 60 , e ) 90
Rationale: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 2 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 2 * ( 2 / 3 ) ) days = > 90 days answer : e"
Answer: e
Python program:
a = 15 * 21
b = a * 8
c = 21 * 2
d = 2 / 3
e = c * d
f = b / e
Problem: if x and y are positive integers and 42 x = 56 y what is the least possible value of xy ?
Options: a ) 14 , b ) 28 , c ) 63 , d ) 196 , e ) 252
Rationale: "42 x = 56 y = > x / y = 4 / 3 = > 3 x = 4 y 3 ( 14 ) = 4 ( 14 ) = > x * y = 196 e"
Answer: e
Python program:
a = 56 + 1
Problem: a train 150 m long is running with a speed of 98 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going
Options: a ) 5 sec , b ) 6 sec , c ) 7 sec , d ) 8 sec , e ) 9 sec
Rationale: "explanation : speed of the train relative to man = ( 98 - 8 ) kmph = ( 90 × 5 / 18 ) m / sec = 25 m / sec time taken by the train to cross the man i = time taken by it to cover 150 m at 25 m / sec = 150 × 1 / 25 sec = 6 sec answer : option b"
Answer: b
Python program:
a = 98 + 8 
b = a * const_0_2778
c = 150 / b
Problem: what is the sum of the greatest common factor and the lowest common multiple of 36 and 56 ?
Options: a ) 512 , b ) 508 , c ) 451 , d ) 516 , e ) 451
Rationale: "prime factorization of 36 = 2 x 2 x 3 x 3 prime factorization of 56 = 2 x 2 x 2 x 7 gcf = 4 lcm = 504 sum = 508 ans : b"
Answer: b
Python program:
a = 36 * 56
b = a / 4
Problem: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 7225 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2887 , c ) 2500 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 7225 = x = 7225 / 2.89 = 2500 therefore , amount invested by raghu is rs . 2500 . answer : c"
Answer: c
Python program:
a = 10 / 100
b = 1 - a
c = 10 / 100
d = 1 + c 
e = b * d
f = 10 / 100
g = 1 - f
h = e + g 
i = h + 1 
j = 7225 / i
Problem: the difference between two parallel sides of a trapezium is 4 cm . perpendicular distance between them is 10 cm . if the area of the trapezium is 250 cm 2 find the lengths of the parallel side
Options: a ) 27 , 23
b ) 25 , 25
c ) 24 , 26
d ) 23 , 29
e ) 24 , 45
Rationale: explanation : let the two parallel sides of the trapezium be a cm and b cm . then , a - b = 4 - - - - - - ( 1 ) and , ( 1 / 2 ) x ( a + b ) x 10 = 475 = > ( a + b ) = ( ( 250 x 2 ) / 10 ) = > a + b = 50 - - - - - - - ( 2 ) solving 1 and 2 , we get : a = 27 , b = 23 so , the two parallel sides are 27 cm and 23 cm . answer : option a
Answer: a
Python program:
a = 250 * 2
b = a / 10
c = b - 4
d = c / 2
e = d + 4 
f = e * 100
g = 250 * 2
h = g / 10
i = h - 4
j = i / 2
k = f + j
Problem: in a box of 8 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 1 / 12 , b ) 5 / 14 , c ) 2 / 13 , d ) 2 / 15 , e ) 1 / 17
Rationale: "first , there are 6 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 8 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 6 c 3 / 8 c 3 = 20 / 56 = 5 / 14 answer is b"
Answer: b
Python program:
a = 8 - 2
b = math.factorial(a)
c = 8 - 2
d = c - 3
e = math.factorial(d)
f = math.factorial(3)
g = e * f
h = b / g
i = math.factorial(8)
j = 8 - 3
k = math.factorial(j)
l = math.factorial(3)
m = k * l
n = i / m
o = h / n
Problem: a sum is divided between a and b in the ratio of 1 : 2 . a purchased a car from his part , which depreciates 14 2 / 7 % per annum and b deposited his amount in a bank , which pays him 20 % interest per annum compounded annually . by what percentage will the total sum of money increase after two years due to this investment pattern ( approximately ) .
Options: a ) 22.48 % , b ) 20.48 % , c ) 24.48 % , d ) 25.48 % , e ) 26.48 %
Rationale: let the total money = 300 a ' s part = 100 b ' s part = 200 after 2 years a ' s part = 73.46 ( as it depreciates by 14.29 % per annum ) after 2 years b ' s part = 288 ( using the compound interest formula , a = p ( 1 + r / n ) ^ nt ) , where p = 200 , r = 0.2 , n = 1 , t = 2 ) so , after 2 years total amount = 361.46 therefore % increase in money = ( 361.46 - 300 ) * 100 / 300 = 20.48 % answer : b
Answer: b
Python program:
a = 20 + 20 
b = a + 7 
c = b + 1 
d = c / 100
e = 20 + d
Problem: how many seconds will a train 100 meters long take to cross a bridge 250 meters long if the speed of the train is 36 kmph ?
Options: a ) 54 sec , b ) 35 sec , c ) 25 sec , d ) 45 sec , e ) 24 sec
Rationale: "d = 100 + 250 = 350 s = 36 * 5 / 18 = 10 mps t = 350 / 10 = 35 sec answer : b"
Answer: b
Python program:
a = 250 + 100 
b = 36 * const_0_2778
c = a / b
Problem: two trains of length 100 m and 160 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 18 sec , b ) 70 sec , c ) 13 sec , d ) 20 sec , e ) 19 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 160 = 260 m . the time required = d / s = 260 / 20 = 13 sec . answer : c"
Answer: c
Python program:
a = 100 + 160 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: pipe a fills a tank in 30 minutes . pipe b can fill the same tank 5 times as fast as pipe a . if both the pipes were kept open when the tank is empty , how much time will it take for the tank to overflow ?
Options: a ) 4 mins , b ) 6 mins , c ) 5 mins , d ) 3 mins , e ) 7 mins
Rationale: "let the total capacity of tank be 90 liters . capacity of tank filled in 1 minute by a = 3 liters . capacity of tank filled in 1 minute by b = 15 liters . therefore , capacity of the tank filled by both a and b in 1 minute = 18 liters . hence , time taken by both the pipes to overflow the tank = 90 / 18 = 5 minutes . answer : c"
Answer: c
Python program:
a = 1 / 30
b = 5 / 30
c = a + b 
d = 1/(c)
Problem: the average age of a class of 15 students is 10 years . if the age of the teacher be included , then the average increased by 1 year . find the age of the teacher ?
Options: a ) 22 , b ) 23 , c ) 26 , d ) 29 , e ) 31
Rationale: "total age of 15 persons = 15 * 10 = 150 years average age of 16 persons = 11 years total age of 16 persons = 16 * 11 = 176 years age of the teacher = 176 - 150 = 26 years answer is c"
Answer: c
Python program:
a = 15 + 1 
b = 10 + 1 
c = a * b
d = 15 * 10
e = c - d
Problem: the sum of digits of a two digit number is 12 , the difference between the digits is 4 . find the number
Options: a ) 84 , b ) 94 , c ) 83 , d ) 72 , e ) none
Rationale: "description : = > x + y = 12 , x - y = 4 adding these 2 x = 16 = > x = 8 , y = 4 . thus the number is 84 answer a"
Answer: a
Python program:
a = 12 + 4 
b = a / 2
c = b * 12
d = 12 + 4 
e = d / 2
f = 12 - e
g = c + f
Problem: find number which is 80 % less than 80 .
Options: a ) 18 , b ) 22 , c ) 28 , d ) 26 , e ) 16
Rationale: "explanation : 80 % less is 20 % of the given number therefore , 20 % of 80 is 16 . answer : e"
Answer: e
Python program:
a = 80 * 80
b = a / 100
Problem: there are some birds in cage , 1 / 3 rd fly away . then 2 / 5 th of the remaining left the cage , then 2 / 3 rd of the remaining left the cage . at last 8 were remaining . how many birds were in total ?
Options: a ) 60 , b ) 27 , c ) 28 , d ) 26 , e ) 91
Rationale: sol : if x birds were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 8 x × 2 / 3 × 3 / 5 × 1 / 3 = 8 x = 60 answer : a
Answer: a
Python program:
a = 3 / 5
b = 2 / 3
c = 1 / 3
d = b * c
e = a * d
f = 8 / e
Problem: x is 3 times as fast as y and working together , they can complete a work in 20 days . in how many days can y alone complete the work ?
Options: a ) 11 days , b ) 80 days , c ) 13 days , d ) 15 days , e ) 19 days
Rationale: x = 3 y x + y = 3 y + y = 4 y these 4 y people together can do the work in 20 days , which means y can alone do the work in 4 * 20 = 80 days . answer : b
Answer: b
Python program:
a = 3 + 1 
b = a * 20
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 9 m wide at the top and 7 m wide at the bottom and the area of cross - section is 560 sq m , the depth of cannel is ?
Options: a ) 39 , b ) 28 , c ) 70 , d ) 80 , e ) 71
Rationale: "1 / 2 * d ( 9 + 7 ) = 560 d = 70 answer : c"
Answer: c
Python program:
a = 9 + 7 
b = a / 2
c = 560 / b
d = c / 7
e = d / 2
Problem: on dividing 199 by a number , the quotient is 11 and the remainder is 1 . find the divisor .
Options: a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 199 - 1 ) / 11 = 198 / 11 = 18 d )"
Answer: d
Python program:
a = 199 / 11
b = math.floor(a)
Problem: of the diplomats who attended a summit conference : 20 spoke french , 32 did not speak hindi and 20 % of the diplomats spoke neither french nor hindi . if 10 % of the diplomats spoke both french and hindi , then how many diplomats attended the conference ?
Options: a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: "2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer"
Answer: d
Python program:
a = 32 - 20
b = 10 / 100
c = a / b
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 59 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320.20 $ , b ) 380.20 $ , c ) 421.20 $ , d ) 451.20 $ , e ) 481.20 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 59 ) = 481.20 hence answer will be ( e )"
Answer: e
Python program:
a = 0 * 65
b = a * 12
Problem: what is the nearest no . to 2304 which is divisible by 21 ?
Options: a ) 2289 , b ) 2310 , c ) 2333 , d ) 2456 , e ) 2309
Rationale: remainder when 2304 is divided by 21 = 15 so , no . should added to make 15 to 21 = 6 no . = 2304 + 6 = 2310 answer b
Answer: b
Python program:
a = 2304 + reminder
Problem: the population of a town is 10000 . it increases annually at the rate of 25 % p . a . what will be its population after 2 years ?
Options: a ) 14000 , b ) 14400 , c ) 14500 , d ) 15625 , e ) 14700
Rationale: formula : 10000 × 125 / 100 × 125 / 100 = 15625 answer : d
Answer: d
Python program:
a = 10000 * 25
b = a / 100
c = b * 2
d = 10000 + c
Problem: when asked what the time is , a person answered that the amount of time left is 4 / 8 of the time already completed . what is the time .
Options: a ) 2 pm , b ) 9 pm , c ) 4 pm , d ) 8 pm , e ) 6 pm
Rationale: "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 4 / 8 x ⇒ x = 20 time is 4 pm answer : c"
Answer: c
Python program:
a = 2 * 12
b = 2 * 12
c = 4 / 8
d = c + 1 
e = b / d
f = a - e
Problem: if x and y are integers , what is the least positive number of 24 x + 20 y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: 24 x + 20 y = 4 ( 6 x + 5 y ) which will be a minimum positive number when 6 x + 5 y = 1 . 6 ( 1 ) + 5 ( - 1 ) = 1 then 4 ( 6 x + 5 y ) can have a minimum positive value of 4 . the answer is c .
Answer: c
Python program:
a = 24 - 20
Problem: of 25 applicants for a job , 14 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 10 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 25 - 3 = 22 aub = a + b - aib aib = 18 + 14 - 22 = 10 answer b"
Answer: b
Python program:
a = 14 + 18 
b = 25 - 3
c = a - b
d = 18 - 14
e = c + d
Problem: the sector of a circle has radius of 28 cm and central angle 90 o . find its perimeter ?
Options: a ) 100 cm , b ) 85 cm , c ) 75 cm , d ) 95 cm , e ) 110 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 90 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 28 ) = 44 + 56 = 100 cm answer : a"
Answer: a
Python program:
a = 28 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 28
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . [ ( 2 - 1 ) / 1 ] * 100 % = 100 % answer : c"
Answer: c
Python program:
a = 100 - 80
b = a - 10
c = 10 / b
d = c * 100
Problem: 3 * 11 + 3 * 12 + 3 * 15 + 11 = ?
Options: a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 151
Rationale: "we have : 3 * 11 = 33 3 * 12 = 36 3 * 15 = 45 all of this is : ( 33 + 36 + 45 ) + 11 = 114 + 11 = 125 correct answer a"
Answer: a
Python program:
a = 3 * 11
b = 3 * 12
c = a + b 
d = 3 * 15
e = c + d 
f = e + 11
Problem: one pump drains one - half of a pond in 8 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: first pump drains 1 / 2 of the tank in 8 hours so 16 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 16 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 16 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 16 + 1 / a ) = 1 / 2 solving u get a = 16 / 15 = 1.1 hence answer is b
Answer: b
Python program:
a = 8 * 2
b = 1 / a
c = 1 - b
d = 1 / c
Problem: there are 2 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 24 , d ) d ) 60 , e ) e ) 100
Rationale: "using anagram method : 4 _ 3 _ 2 _ 1 r _ r _ b _ b so . . 4 ! / number of repeated letters ( 2 ! ) ( 2 ! ) = 6 ans : d"
Answer: d
Python program:
a = math.factorial(2)
b = math.factorial(2)
c = a * b
Problem: the speed of a car is 50 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 79 kmph , b ) 85 kmph , c ) 55 kmph , d ) 23 kmph , e ) 14 kmph
Rationale: "s = ( 55 + 60 ) / 2 = 55 kmph answer : c"
Answer: c
Python program:
a = 50 + 60 
b = a / 2
Problem: the top and bottom of a tower were seen to be at angles of depression 30 ° and 60 ° from the top of a hill of height 100 m . find the height of the tower
Options: a ) 64.67 m , b ) 66.67 m , c ) 68.67 m , d ) 56.67 m , e ) 46.67 m
Rationale: by making a diagram ac represents the hill and de represents the pole given that ac = 100 m anglexad = angleadb = 30 ° ( ∵ ax | | bd ) anglexae = angleaec = 60 ° ( ∵ ax | | ce ) let de = h then , bc = de = h , ab = ( 100 - h ) ( ∵ ac = 100 and bc = h ) , bd = ce tan 60 ° = acce = > 3 √ = 100 ce = > ce = 1003 √ - - - ( 1 ) tan 30 ° = abbd = > 13 √ = 100 − hbd = > 13 √ = 100 − h ( 1003 √ ) ( ∵ bd = ce and substituted the value of ce from equation 1 ) = > ( 100 − h ) = 13 √ × 1003 √ = 1003 = 33.33 = > h = 100 − 33.33 = 66.67 m i . e . , the height of the pole = 66.67 m answer : b
Answer: b
Python program:
a = const_0_33 * 100
b = 100 - a
Problem: the age of the daughter is same as the digit in the mother ' s age , but in reverse order . in thirteen years mother will be twice as old as daughter will be then . what is the difference in their current age ?
Options: a ) 15 , b ) 23 , c ) 27 , d ) 46 , e ) 32
Rationale: daughter ' s age = 10 x + y so mother ' s age = 10 y + x . . after 13 years , 10 x + y + 13 = 2 * ( 10 y + x + 13 ) . . . . so 13 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 4 . . . so ages are 41 and 14 and ans as found correctly by u is c . . 27
Answer: c
Python program:
a = 12 + 1 
b = 10 - 1
c = b + 10 
d = a + c 
e = d / 4
f = e / 2
g = f * 10
h = g + 1 
i = 12 + 1 
j = 10 - 1
k = j + 10 
l = i + k 
m = l / 4
n = m / 2
o = 10 + n 
p = h - o
Problem: working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel four 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 ) 5 , 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 / 4 and w = 4 s then we have 1 / ( 4 * s ) + 1 / s = 1 / 4 < = > 5 / ( 4 * s ) = 1 / 4 < = > s = 5 ans : c"
Answer: c
Python program:
a = 2 * 4
b = 1/(a)
c = b + 1 
d = c * 3
e = 2 * 4
f = d * e