euclaise/mathqa_programs huggingface dataset:
Problem: two trains 100 m and 60 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 5.76 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 20.8 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 100 + 60 = 160 m . required time = 160 * 9 / 250 = 5.76 = 5.76 sec . answer : b"
Answer: b
Python program:
a = 100 + 60 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: the price of lunch for 15 people was $ 207.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.00 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: "if the amount spent excluding the gratuity was x , then x ( 1.15 ) = 207 = > x = 207 / 1.15 = 180 then the average price per person = 180 / 15 = 12 option ( b )"
Answer: b
Python program:
a = 100 + 15 
b = 207 / 0
c = b * 100
d = 1 / 15
e = c * d
Problem: find the missing figures : 0.50 % of ? = 0.12
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let 0.50 % of x = 0.12 . then , 0.50 * x / 100 = 0.12 x = [ ( 0.12 * 100 ) / 0.50 ] = 24 . answer is e ."
Answer: e
Python program:
a = 0 / 50
b = 0 / 12
Problem: a no . when divided by 220 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 11 , e ) 15
Rationale: "220 + 43 = 263 / 17 = 8 ( remainder ) b"
Answer: b
Python program:
a = 220 + 43 
b = a / 17
Problem: shipment - - - - - - no . of defective chips / shipment - - - total chips in shipment s 2 - - - - - - - - - - - - - - 5 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12000 s 3 - - - - - - - - - - - - - - 6 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 18000 s 4 - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16000 a computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts s 1 , s 2 , s 3 and s 4 comined as shown in the table above . what is the expected number q of defective chips in a shipment of 60000 chips ?
Options: a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 25
Rationale: i agree with your solution = 20 . but the question is : there are different combination to get 60000 chips . for example : 1 * s 3 + 2 * s 4 + 2 * s 2 . in this way , we ship 60000 chips with only 6 + 4 * 2 + 2 * 2 = 18 defective chips , better than the average of 20 . the question is to find the expected number q of defective chips , i guess it assume the minimum # , therefore it might not be 20 .
Answer: b
Python program:
a = 60000 - 18000
b = a - 16000
c = b - 12000
d = 16000 - c
e = d / 100
Problem: if 2 x + y = 7 and x + 2 y = 5 , then 8 xy / 3 = ?
Options: a ) a ) 1 , b ) b ) 8 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 8 * 3 * 1 ) / 3 = 24 / 3 = 8 b"
Answer: b
Python program:
a = 7 * 2
b = a - 5
c = 2 * 2
d = c - 1
e = b / d
f = 7 * 2
g = f - 5
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 7 - k
m = e + l 
n = m / 8
Problem: the maximum number of students among them 640 pens and 520 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "number of pens = 640 number of pencils = 520 required number of students = h . c . f . of 640 and 520 = 40 answer is a"
Answer: a
Python program:
a = math.gcd(640, 520)
Problem: a certain airline ' s fleet consisted of 80 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let x be the number of years . 4 x > 80 - 3 x 7 x > 80 x > 11 + 3 / 7 the answer is d ."
Answer: d
Python program:
a = 3 + 4 
b = 80 / a
Problem: if the numbers 1 to 96 are written on 96 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 96 , d ) 1 , e ) 2
Rationale: there are 25 primes , 70 composite numbers from 1 to 96 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 96 . answer : c
Answer: c
Python program:
a = 1 / 96
Problem: sandy walked 25 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 25 meters . she then turned to her right and walked 12 meters . what distance is she from the starting point and in which direction ?
Options: a ) 32 meters east , b ) 32 meters north , c ) 32 meters west , d ) 42 meters east , e ) 52 meters west
Rationale: "the net distance is 20 + 12 = 32 meters to the east . the answer is a ."
Answer: a
Python program:
a = 25 + 12
Problem: how many liters of water must be evaporated from 50 liters of a 1 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 35 , b ) 40 , c ) 42 , d ) 45 , e ) 48
Rationale: 1 % of a 50 liter solution is 0.5 l which is 10 % of the solution at the end . the solution at the end must be 5 l . we need to evaporate 45 liters . the answer is d .
Answer: d
Python program:
a = 50 / 100
b = a * 10
c = 50 - b
Problem: raman mixed 27 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?
Options: a ) 129 , b ) 287 , c ) 190 , d ) 188 , e ) 112
Rationale: "explanation : cp per kg of mixture = [ 27 ( 150 ) + 36 ( 125 ) ] / ( 27 + 36 ) = rs . 135.71 sp = cp [ ( 100 + profit % ) / 100 ] = 135.71 * [ ( 100 + 40 ) / 100 ] = rs . 190 . answer : c"
Answer: c
Python program:
a = 27 * 150
b = 36 * 125
c = a + b 
d = 36 + 27 
e = c / d
f = 27 * 150
g = 36 * 125
h = f + g 
i = 36 + 27 
j = h / i
k = 40 / 100
l = j * k
m = e + l
Problem: the average of 50 numbers id 56 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.35 , b ) 33.25 , c ) 22.25 , d ) 51.35 , e ) 56.25
Rationale: explanation : total of 50 numbers = ( 50 × 56 ) = 2800 total of 48 numbers = ( 2800 - ( 45 + 55 ) ] = 2700 required average = 2700 / 48 = 56.25 answer : e
Answer: e
Python program:
a = 50 * 56
b = 45 + 55 
c = a - b
d = 50 - 2
e = c / d
Problem: a set consists of 12 numbers , all are even or multiple of 5 . if 7 numbers are even and 14 numbers are multiple of 5 , how many numbers is multiple of 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 9
Rationale: "{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 12 = 7 + 14 - { both } + 0 ; { both } = 9 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : e ."
Answer: e
Python program:
a = 12 - 14
Problem: sum of the squares of 3 no . is 149 and the sum of their products taken two at a time is 70 . find the sum ?
Options: a ) 17 , b ) 19 , c ) 21 , d ) 13 , e ) 18
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 149 + 2 * 70 a + b + c = â ˆ š 289 = 17 answer a"
Answer: a
Python program:
a = 70 * 2
b = 149 + a 
c = math.sqrt(b)
Problem: if x and y are positive integers and x = 5 y + 2 , what is the remainder when x is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that x and y are positive integers and x = 5 y + 2 . we ' re asked for the remainder when x is divided by 5 . if . . . . y = 1 x = 7 7 / 5 = 1 remainder 2 final answer : c"
Answer: c
Python program:
a = 2 + 1 
b = a / 5
Problem: if , 1 * 3 * 5 = 16 3 * 5 * 7 = 38 5 * 7 * 9 = 68 then find , 7 * 9 * 11 = ?
Options: a ) 106 , b ) 49 , c ) 68 , d ) 38 , e ) 55
Rationale: a 106 ( 11 * 9 ) + 7 = 106
Answer: a
Python program:
a = 9 * 11
b = a + 7
Problem: a is twice as good a workman as b and they took 7 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 88 days , c ) 21 days , d ) 11 days , e ) 13 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 7 x = 1 / 21 = > 21 days answer : c"
Answer: c
Python program:
a = 2 + 1 
b = 7 * a
c = b / 2
d = c * 2
Problem: points a , b , c , and d , in that order , lie on a line . if ab = 2 cm , ac = 4 cm , and bd = 6 cm , what is cd , in centimeters ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "putting a value to each point , lets use the following : a - 0 b - 2 ( ab = 2 ) c - 4 ( ac = 4 ) d - 8 ( bd = 6 ) cd is 8 - 4 = 4 . ans d"
Answer: d
Python program:
a = 4 - 2
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 844 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 728 , e ) s . 760
Rationale: "s . i . for 1 year = rs . ( 844 - 815 ) = rs . 29 . s . i . for 3 years = rs . ( 29 x 3 ) = rs . 87 . principal = rs . ( 815 - 87 ) = rs . 728 . answer : option d"
Answer: d
Python program:
a = 844 - 815
b = a * 3
c = b / 4
d = 815 - c
Problem: a side of beef lost 40 percent of its weight in processing . if the side of beef weighed 240 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 400 , c ) 737 , d ) 840 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 60 / 100 ) * x = 240 = > x = ( 240 * 100 ) / 60 = 400 answer b"
Answer: b
Python program:
a = 240 * 100
b = 100 - 40
c = a / b
Problem: 36 men can complete a piece of work in 18 days . in how days will 27 men can complete the work ?
Options: a ) 18 , b ) 20 , c ) 17 , d ) 24 , e ) 21
Rationale: "let the required number of days be x less men , more days ( indirect proportion ) 27 : 36 : : 18 : x 27 x = 36 * 18 x = ( 36 * 18 ) / 27 x = 24 days option is d"
Answer: d
Python program:
a = 18 * 36
b = a / 27
Problem: a trader bought a car at 50 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 62 % , c ) 12 % , d ) 19 % , e ) 71 %
Rationale: "original price = 100 cp = 95 s = 95 * ( 180 / 100 ) = 112 100 - 171 = 71 % answer : e"
Answer: e
Python program:
a = 100 - 50
b = 100 + 80 
c = a * b
d = c / 100
e = d / 100
f = e - 1
g = f * 100
Problem: renu can do a piece of work in 8 days , but with the help of her friend suma , she can do it in 3 days . in what time suma can do it alone ?
Options: a ) 4.8 , b ) 1.2 , c ) 4.4 , d ) 4.6 , e ) 4.7
Rationale: "renu â € ™ s one day â € ™ s work = 1 / 8 suma â € ™ s one day â € ™ s work = 1 / 3 - 1 / 8 = 5 / 24 suma can do it alone in 4.8 days . answer : a"
Answer: a
Python program:
a = 1 / 3
b = 1 / 8
c = a - b
d = 1/(c)
Problem: what is the sum of the odd integers from 35 to 65 , inclusive ?
Options: a ) 800 , b ) 550 , c ) 555 , d ) 600 , e ) 605
Rationale: "the mean is 50 . sum = mean ( # of elements ) there are 16 odd numbers between 35 - 65 inclusive . 16 * 50 = 800 a"
Answer: a
Python program:
a = 35 * 65
b = a / 4
Problem: excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 36 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 20 min , b ) 8 min , c ) 9 min , d ) 10 min , e ) 11 min
Rationale: "due to stoppages , it covers 18 km less . time taken to cover 18 km = ( 18 / 54 ) x 60 = 20 min answer : a"
Answer: a
Python program:
a = 54 - 36
b = a / 54
c = const_60 * b
Problem: a worker can load one truck in 6 hours . a second worker can load the same truck in 5 hours . if both workers load one truck simultaneously while maintaining their constant rates , approximately how long , in hours , will it take them to fill one truck ?
Options: a ) 2.7 , b ) 2.9 , c ) 3.1 , d ) 3.3 , e ) 3.5
Rationale: "the workers fill the truck at a rate of 1 / 6 + 1 / 5 = 11 / 30 of the truck per hour . then the time to fill one truck is 30 / 11 which is about 2.7 hours . the answer is a ."
Answer: a
Python program:
a = 1 / 6
b = 1 / 5
c = a + b 
d = 1/(c)
Problem: which is equal to 11 ?
Options: a ) 1.1 , b ) - 11 , c ) 11 / 11 , d ) 11 / 1 , e ) 1 / 11
Rationale: "11 / 1 is equal to 11 . answer : d"
Answer: d
Python program:
a = 11 / 4
b = a / 3
c = b / 4
d = c / 3
e = d / 2
f = e / 2
Problem: the speed of a train is 102 kmph . what is the distance covered by it in 30 minutes ?
Options: a ) 50 kmph , b ) 51 kmph , c ) 41 kmph , d ) 61 kmph , e ) 21 kmph
Rationale: "102 * 30 / 60 = 51 kmph answer : b"
Answer: b
Python program:
a = 30 / const_60
b = a * 102
Problem: a rectangular of certain dimensions is chopped off from one corner of a larger rectangle as shown . ab = 8 cm and bc = 4 cm . the perimeter of the figure abcpqra ( in cm ) is :
Options: a ) 24
b ) 28
c ) 36
d ) 48
e ) none of these
Rationale: solution required perimeter = ( ab + bc + cp + pq + qr + ra ) = ab + bc + ( cp + qr ) + ( pq + ra ) = ab + bc + ab + bc = 2 ( ab + bc ) = [ 2 ( 8 + 4 ) ] cm = 24 cm . answer a
Answer: a
Python program:
a = 8 + 4 
b = a * 2
Problem: 20 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 20 * 10 / 40 = 5 answer is e"
Answer: e
Python program:
a = 20 * 10
b = a / 40
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 110 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,210
Rationale: "10 / 100 p = 110 > > p = 110 * 100 / 10 = 1100 1100 - 110 = 990 answer : b"
Answer: b
Python program:
a = 100 / 10
b = 110 * a
c = b - 110
Problem: in a trapezium abcd , ab is parallel to dc , ab = 3 * dc , and the diagonals of the trapezium intersect at o . the ratio of the area of ∆ ocd to the area of ∆ oab is :
Options: a ) 1 : 9
b ) 1 : 3
c ) 3 : 1
d ) 1 : 10
e ) can not be determined
Rationale: triangles are similar , so ratio will be 1 : 9 a
Answer: a
Python program:
a = 1 / 3
b = 1 / 3
c = a * b
Problem: when 1 / 10 percent of 6,000 is subtracted from 1 / 10 of 6,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 450 , d ) 495 , e ) 694
Rationale: "we can break this problem into two parts : 1 ) what is 1 / 10 percent of 6,000 ? 2 ) what is 1 / 10 of 6,000 ? to calculate 1 / 10 percent of 6,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 6,000 = 1 / 1,000 x 6,000 = 6 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 5,000 . to do this we simply multiply 1 / 10 by 6,000 . 1 / 10 x 6,000 = 600 the answer to part 1 is 6 , and the answer to part 2 is 600 . their difference is 600 – 6 = 694 . answer e ."
Answer: e
Python program:
a = 3 + 4 
b = a * 1000
c = 1 / 10
d = b * c
e = 1 / 10
f = e / 100
g = 3 + 4 
h = g * 1000
i = f * h
j = d - i
Problem: if there are 200 questions in a 3 hr examination . among these questions are 10 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
Options: a ) 17.14286 min , b ) 62 min , c ) 70.1346 min , d ) 74 min , e ) 76.1346 min
Rationale: x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 190 x + 10 * 2 x = 180 x = 180 / 210 x = 0.72 time taken for type a problem = 10 * 2 * 0.857143 = 17.14286 min answer : a
Answer: a
Python program:
a = 3 * const_60
b = 200 - 10
c = 2 * 10
d = b + c 
e = a / d
f = 2 * e
g = f * 10
Problem: working individually , jane can bake cakes for 4 hours and roy can bake cakes in 5 hours . if jane and roy work together but independently at the task for 2 hours , at which point roy leaves , how many remaining hours will it take jane to complete the task alone ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 4 , d ) 1 / 4 , e ) 1 / 5
Rationale: in first 2 hrs roy will finish 2 / 5 = 2 / 5 of work and jane will finish 2 / 4 work so total 2 / 5 + 1 / 2 = 9 / 10 work is finished and 1 - 9 / 10 = 1 / 10 work remaining . now jane will take ( 1 / 10 ) * 4 = 2 / 5 hrs to finish it . so answer is b .
Answer: b
Python program:
a = 4 / 10
Problem: the arithmetic mean of set x is zero . if y = { - 2.22 ; - 1.96 ; - 1.68 ; 1.62 ; 1.94 ; 2.16 } is the subset of x consisting of all those elements in x which are more than two but less than 3 standard deviations away from the arithmetic mean of x , what could be equal to the standard deviation of x ?
Options: a ) 0.54 , b ) 0.77 , c ) 0.82 , d ) 0.97 , e ) 1.62
Rationale: this is a fairly straightforward question that can be solved quickly by just applying the options we are provided with mean , m = 0 and y = { - 2.22 ; - 1.96 ; - 1.68 ; 1.62 ; 1.94 ; 2.16 } is the subset of s y consists of all those elements in x that are more than 2 but less than 3 xds away from the arithmetic mean of x if an element is 1 xd away from the mean , we can write it as either m + xd or m - xd similarly , if an element is 2 xds away from the mean , we can write it as either m + 2 * xd or m - 2 * xd so , if these elements lie within 2 and 3 xds of mean , m = 0 we can find which one of these values of xd satisfies each value within y only xd = 0.77 does answer : b
Answer: b
Python program:
a = 2 / 22
Problem: what is the sum of odd integers from 25 to 85 , inclusive ?
Options: a ) 1,705 , b ) 1,500 , c ) 1,240 , d ) 1,120 , e ) 1,100
Rationale: number of odd integers = ( 85 - 25 ) / 2 + 1 = 60 / 2 + 1 = 31 sum of odd integers = ( 25 + 85 ) / 2 * 31 = 1705 answer a
Answer: a
Python program:
a = 85 / 85
Problem: carrie likes to buy t - shirts at the local clothing store . they cost $ 9.95 each . one day , she bought 25 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 248.75 , c ) $ 200 , d ) $ 171.6 , e ) $ 190
Rationale: $ 9.95 * 25 = $ 248.75 . answer is b .
Answer: b
Python program:
a = 25 * 9
b = math.floor(a)
Problem: evaluate the sum 1 - 2 + 3 - 4 + 5 - 6 + . . . + 997 - 998 + 999 - 1000
Options: a ) - 500 , b ) - 1000 , c ) - 999 , d ) - 1001 , e ) 500500
Rationale: one groups the first two terms and each successive two terms to obtain a sum of 500 expressions each of which is - 1 . the answer is - 500 correct answer a
Answer: a
Python program:
a = 1000 / 2
Problem: a line has a slope of 3 / 4 and intersects the point t ( - 12 , - 39 ) . at which point does this line intersect the x - axis ?
Options: a ) ( 40,0 ) , b ) ( 30,0 ) , c ) ( 0,40 ) , d ) ( 40,30 ) , e ) ( 0,30 )
Rationale: "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point t of intersection is ( 40,0 ) . a is the correct answer ."
Answer: a
Python program:
a = negate - (
b = negate * (
c = 3 / 4
d = a / b
e = negate * (
Problem: the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 8337 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6725 , b ) rs . 6727 , c ) rs . 6908 , d ) rs . 6725 , e ) rs . 6947.5
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8337 ( 100 / 120 ) = rs . 6947.5 answer : e"
Answer: e
Python program:
a = 20 / 100
b = 1 + a 
c = 8337 / b
Problem: two drivers began their journey with the same amount of petrol in their cars at the same time . the only difference is that the first driver � s car could drive 4 hours in that amount of petrol and the second one could drive 5 hours . however , they only drove for some time and found that the amount of petrol that was left in one of the cars was 4 times the petrol left in the other one . for how long had they driven at this point of time ?
Options: a ) 3.75 hours , b ) 5.45 hours , c ) 7.10 hours , d ) 4.75 hours , e ) 3.33 hours
Rationale: a 3.75 hours while you can solve it as you like , a simple mathematical equation can be used to find out . let m be the amount of petrol initially . let n be the time for which they drove . according to the question , the amount of petrol used by first car in n hours = mn / 4 the amount of petrol used by second car in n hours = mn / 5 hence , the amount of petrol left in the first car = ( m - mn / 4 ) the amount of petrol left in the second car = ( m - mn / 5 ) as per the details given in the question , we can form the below equation : m - mn / 5 = 4 ( m - mn / 4 ) n = 15 / 4 or 3.75 hours . hence , both the drivers have driven the car for 3.75 hours at that particular time .
Answer: a
Python program:
a = 4 - 1
b = 1 / 4
c = b * 4
d = 1 / 5
e = c - d
f = a / e
Problem: the ratio of two numbers is 5 : 9 . if each number is decreased by 5 , the ratio becomes 5 : 11 . find the numbers .
Options: a ) 30 , 19 , b ) 21 , 37 , c ) 15 , 34 , d ) 15 , 27 , e ) none of these
Rationale: "explanation : let the two numbers be 5 x and 9 x . ( 5 x - 5 ) / ( 9 x - 5 ) = 5 : 11 ( 5 x - 5 ) * 11 = ( 9 x - 5 ) * 5 55 x – 55 = 45 x – 25 10 x = 30 x = 3 therefore , the numbers are 15 and 27 . answer : d"
Answer: d
Python program:
a = 5 ** 9
b = 5 ** 2
c = 9 ** 9
d = b + c 
e = a + d 
f = 5 / e
g = math.sqrt(f)
Problem: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 11 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 190 , c ) 132 , d ) 170 , e ) 60
Rationale: "c 132 sum = ( n x n ) + n hence , 11 x 11 = 121 + 11 = 132"
Answer: c
Python program:
a = 11 + 1 
b = a * 11
Problem: the average height of 12 girls out of a class of 20 is 161 cm . and that of the remaining girls is 158 cm . the average height of the whole class is :
Options: a ) 142.3 cms , b ) 162.3 cms , c ) 160.5 cms , d ) 142.8 cms , e ) 159.8 cms
Rationale: "explanation : average height of the whole class = ( 12 × 161 + 8 × 158 / 20 ) = 159.8 cms answer e"
Answer: e
Python program:
a = 161 * 12
b = 158 * 10
c = a + b 
d = c / 20
Problem: find out the c . i on rs . 9000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 550.87 , b ) 506.07 , c ) 506.04 , d ) 506.03 , e ) 306.01
Rationale: "a = 9000 ( 51 / 50 ) 3 = 9550.87 9000 - - - - - - - - - - - 550.87 answer : a"
Answer: a
Python program:
a = 4 / 100
b = 1 + a 
c = 3 / 2
d = b ** c
e = 9000 * d
f = e - 9000
Problem: the length of rectangle is thrice its breadth and its perimeter is 56 m , find the area of the rectangle ?
Options: a ) 432 , b ) 212 , c ) 252 , d ) 992 , e ) 147
Rationale: "2 ( 3 x + x ) = 56 l = 21 b = 7 lb = 21 * 7 = 147 answer : e"
Answer: e
Python program:
a = 3 * 2
b = 1 * 2
c = a + b 
d = 56 / c
e = d * 3
f = 3 * 2
g = 1 * 2
h = f + g 
i = 56 / h
j = e * i