euclaise/mathqa_programs huggingface dataset:
Problem: in a box of 10 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 4 / 9 , b ) 5 / 11 , c ) 7 / 15 , d ) 9 / 22 , e ) 12 / 35
Rationale: "# defective pens = 3 # good pens = 7 probability of the 1 st pen being good = 7 / 10 probability of the 2 nd pen being good = 6 / 9 total probability = 7 / 10 * 6 / 9 = 7 / 15 the answer is c ."
Answer: c
Python program:
a = 10 - 3
b = a / 10
c = 10 - 3
d = c - 1
e = 10 - 1
f = d / e
g = b * f
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b , the present age of b is :
Options: a ) 19 , b ) 29 , c ) 39 , d ) 49 , e ) none of these
Rationale: "explanation : let b ' s present age = x years . then , a ' s present age = ( x + 9 ) years . ( x + 9 ) + 10 = 2 ( x - 10 ) = > x + 19 = 2 x - 20 = > x = 39 . answer : c"
Answer: c
Python program:
a = 2 * 10
b = a + 10 
c = b + 9
Problem: in the recent , climate conference in new york , out of 700 men , 500 women , 800 children present inside the building premises , 20 % of the men , 40 % of the women and 10 % of the children were indians . find the percentage of people who were not indian ?
Options: a ) 77 % , b ) 73 % , c ) 79 % , d ) 83 % , e ) none
Rationale: solution : number of indians men present there = 700 * 20 / 100 = 140 indian women = 500 * 40 / 100 = 200 indian children = 800 * 10 / 100 = 80 . total member present in climate conference = 700 + 500 + 800 = 2000 total indian = 200 + 140 + 80 = 420 hence , % of indian present there = 420 * 100 / 2000 = 21 % % of people who were not indian = 100 - 42 = 79 % . answer c
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = 700 * b
d = 40 / 100
e = 1 - d
f = 500 * e
g = c + f 
h = 10 / 100
i = 1 - h
j = 800 * i
k = g + j 
l = 700 + 500 
m = l + 800 
n = k / m
o = n * 100
Problem: a can do a work in 9 days and b can do the same work in 18 days . if they work together , in how many days will they complete the work ?
Options: a ) 6 days , b ) 7 days , c ) 5 days , d ) 3 days , e ) 2 days
Rationale: one day ' s work of a and b = 1 / 9 + 1 / 8 = ( 2 + 1 ) / 18 = 1 / 6 so , the time taken to complete the work is 6 days . answer : a
Answer: a
Python program:
a = 1 / 9
b = 1 / 18
c = a + b 
d = 1 / c
Problem: the sum of the numbers is 660 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 48 , b ) 54 , c ) 72 , d ) 84 , e ) 180
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 660 11 x / 3 = 660 x = 180 answer : e"
Answer: e
Python program:
a = 660 * 3
b = 10 + 1 
c = a / b
Problem: jim drove 642 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 113 miles , b ) 432 miles , c ) 558 miles , d ) 887 miles , e ) 767 miles
Rationale: "the number of miles to drive to finish his journey is given by 1200 - 642 = 558 miles correct answer c"
Answer: c
Python program:
a = 1200 - 642
Problem: working together , jose and jane can complete an assigned task in 30 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 45 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose
Options: a ) 90 days , b ) 30 days , c ) 60 days , d ) 65 days , e ) 36 days
Rationale: "assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 30 30 ( x + y ) = xy next , we ' re told 1 job takes 45 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 45 x + y = 90 so xy = 30 * 90 = 2700 the answer choices are : 90 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 90 days for jose and 30 days for jane . answer : a"
Answer: a
Python program:
a = 3 * 30
Problem: two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 8 seconds , the speed of each train ( in km / hr ) is
Options: a ) 42 , b ) 36 , c ) 28 , d ) 20 , e ) 54
Rationale: "explanation : distance covered = 120 + 120 = 240 m time = 12 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 8 = 30 m / s speed of each train = v = 30 / 2 = 15 m / s = 15 × 36 / 10 km / hr = 54 km / hr answer : option e"
Answer: e
Python program:
a = 120 + 120 
b = a / 8
c = b / 2
d = const_3_6 * c
Problem: the floor of a rectangular room is 17 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 124 m 2 , b ) 132 m 2 , c ) 148 m 2 , d ) 152 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 21 ã — 16 = 336 m 2 area of the inner rectangle = 17 ã — 12 = 204 m 2 required area = ( 336 â € “ 204 ) = 132 m 2 answer b"
Answer: b
Python program:
a = 2 * 2
b = a + 17 
c = 2 * 2
d = 12 + c 
e = rectangle_area - (
Problem: how many cubes of 2 cm edge can be cut out of a cube of 24 cm edge
Options: a ) 1136 , b ) 1728 , c ) 1216 , d ) 1484 , e ) none of these
Rationale: "explanation : number of cubes = ( 24 x 24 x 24 ) / ( 2 x 2 x 2 ) = 1728 answer : b"
Answer: b
Python program:
a = volume_cube / (
Problem: a sum fetched total simple interest of 4016.25 at the rate of 14 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 5737.5 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 70 % of p = 4016.25 or , p = 5737.5 answer a"
Answer: a
Python program:
a = 100 * 4016
b = 14 * 5
c = a / b
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 21 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 288 , b ) 225 , c ) 881 , d ) 1277 , e ) 121
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 21 = 315 m . let the length of the platform be x m . then , ( x + 315 ) / 36 = 15 = > x = 225 m . answer : b"
Answer: b
Python program:
a = 54 * const_0_2778
b = 21 * a
Problem: seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 24 % ryegrass and 75 % fescue . if a mixture of x and y contains 36 % ryegrass , what percent of the weight of the mixture is from mixture x ?
Options: a ) 25 % , b ) 40 % , c ) 60 % , d ) 75 % , e ) 90 %
Rationale: 36 % is 12 % - points above 25 % and 4 % - points below 40 % . thus the ratio of mixture y to mixture x is 1 : 3 . the percent of mixture x is 3 / 4 = 75 % . the answer is d .
Answer: d
Python program:
a = 24 + 1 
b = 36 - a
c = 40 / 100
d = 24 + 1 
e = d / 100
f = c - e
g = b / f
Problem: hcf of two numbers is 15 and their lcm is 180 . if their sum is 105 , then the numbers are
Options: a ) 30 and 75 , b ) 35 and 70 , c ) 40 and 65 , d ) 45 and 60 , e ) 55 and 70
Rationale: "explanation : let the numbers be 15 a and 15 b . then , 15 a + 15 b = 105 or a + b = 7 . . ( i ) lcm = 15 ab = 180 ab = 12 . . ( ii ) solving equations ( i ) and ( ii ) , we get a = 4 , b = 3 so , the numbers are 15 × 4 and 15 × 3 , i . e . , 60 and 45 answer : d"
Answer: d
Python program:
a = 180 / 15
Problem: lloyd normally works 7.5 hours per day and earns $ 5.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 1.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
Options: a ) $ 33.75 , b ) $ 47.25 , c ) $ 51.75 , d ) $ 54.00 , e ) $ 66.00
Rationale: daily working hour * regular rate + overtime * increased rate 7.5 * 5.5 + 3 * 5.5 * 1.5 = 66.00 answer e
Answer: e
Python program:
a = 7 * 5
b = 10 - 5
c = b * 1
d = c * 5
e = a + d
Problem: the cyclist going at a constant rate of 20 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 60 miles per hour . the motor - cyclist stops to wait for the cyclist 10 minutes after passing her , while the cyclist continues to travel at constant rate , how many minutes must the motor - cyclist wait until the cyclist catches up ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 40
Rationale: "for the 10 minutes the motor - cyclist continues to overtake the cyclist , she is going at 40 miles per hour faster than the cyclist . once the motor - cyclist stops , the cyclist is going at 20 miles per hour while the motor - cyclist is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 40 / 20 * 10 or 20 minutes answer is ( b )"
Answer: b
Python program:
a = 60 / 4
b = 20 / 4
c = a - b
d = c * const_60
e = d / 20
Problem: how many 4 digit numbers divisible by 4 can be made with digits 1 , 2 , 3 , 4 , 5 if the repetition of digits is not allowed ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: a number is divisible by 4 if the last 2 numbers are divisible by 4 ( divisible by 2 twice ) ending can be 12 24 32 42 52 case : ending with 12 , 24,32 , 42,54 first digit - 3 choices second digit - 2 choices third digit - 1 choice fourth digit - 1 choice 6 possible choices for each ending ( e . g . 3412,3512 , 3212 , 4512 , 5312 , 5412 ) total number of 4 digit numbers divisible by 4 = 6 * 5 = 30 answer : c
Answer: c
Python program:
a = 3 * 2
b = a * 4
c = b + 5
Problem: x and y are positive integers . when x is divided by 17 , the remainder is 3 , and when x is divided by 19 , the remainder is 1 . when y is divided by 14 , the remainder is 5 , and when y is divided by 21 , the remainder is 12 . what is the least possible value of y - x ?
Options: a ) 15 , b ) 13 , c ) 11 , d ) 14 , e ) 18
Rationale: when x is divided by 17 , the remainder is 3 : so , the possible values of x are : 3 , 20 , 37,54 , etc . when x is divided by 19 , the remainder is 1 : so , the possible values of x are : 1,20 . . . stop . since both lists include 20 , the smallest possible value of x is 20 . when y is divided by 14 , the remainder is 5 : so , the possible values of y are : 5 , 19 , 33,47 etc . when y is divided by 21 , the remainder is 12 : so , the possible values of y are : 12 , 33 , . . . stop . since both lists include 33 , the smallest possible value of y is 33 since the smallest possible values of x and y are 20 and 33 respectively , the smallest possible value of y - x is 13 . so , b is the correct answer to the original question .
Answer: b
Python program:
a = 14 * 2
b = a + 5 
c = 3 + 17 
d = b - c
Problem: how many hours are there in 1200 minutes ?
Options: a ) 10 , b ) 20 , c ) 85 , d ) 86 , e ) 88
Rationale: we know that there are 60 minutes in 1 hour . divide the number of minutes by the number of minutes in 1 hour . we get , divide 1200 by 601200 ÷ 60 = 20 so there are 20 hours in 1200 minutes . answer is b
Answer: b
Python program:
a = 1200 / const_60
Problem: how many terminating zeroes t does 200 ! have ?
Options: a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
Rationale: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
Answer: c
Python program:
a = 4 + 1 
b = 200 / a
c = 4 + 1 
d = 4 + 1 
e = c * d
f = 200 / e
g = b + f
Problem: brindavan express leave chennai central station every day at 07.50 am and goes to bangalore city railway station . this train is very popular among the travelers . on 25 th july 2012 number of passengers traveling by i class and ii class was in the ratio 1 : 4 . the fare for this travel is in the ratio 3 : 1 . the total fare collected was rs . 224000 / . ( rs . two lakhs 20 4 1000 only ) . what was the fare collected from i class passengers on that day ?
Options: a ) rs . 32000 , b ) rs . 96000 , c ) rs . 128000 , d ) rs . 500000 , e ) none of these
Rationale: solution : let the number of passenger traveling by first class be x . then , number of passenger traveling by second class will be 4 x . but the fare is in the ratio 3 : 1 in other words , if 3 y fare is collected per i class passenger , y would be collected per ii class passenger . fares of i class passengers : fares of ii class passengers = x * 3 y : 4 x * y = 3 : 4 the above ratio can be interpreted as follows . if total fare is 3 + 4 = 7 , then i class passengers should pay rs . 3 similarly , we can calculate the fare of i class passengers when total was 224000 total fare i class fare 7 3 224000 ? = 224000 * ( 3 / 7 ) = rs . 96000 . answer : option b
Answer: b
Python program:
a = 4 + 3 
b = 3 / a
c = 224000 * b
Problem: worker a takes 5 hours to do a job . worker b takes 15 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 15 / 4 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 80 / 9
Rationale: "one day work of a = 1 / 5 one day work of b = 1 / 15 so one day work of a and b together = 1 / 5 + 1 / 15 = 4 / 15 so total days required = 15 / 4 answer : a"
Answer: a
Python program:
a = 1 / 5
b = 1 / 15
c = a + b 
d = 1 / c
Problem: there are 14 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 288 , b ) 267 , c ) 261 , d ) 211 , e ) 240
Rationale: "the total number of stations = 16 from 16 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 16 p ₂ ways . 16 p ₂ = 16 * 15 = 240 . answer : e"
Answer: e
Python program:
a = 14 + 1 
b = 14 + 1 
c = b + 1 
d = a * c
Problem: in a theater , the first row has 12 seats and each row has 2 more seats than previous row . if the last row has 48 seats , what is the total number of seats in the theater ?
Options: a ) 550 , b ) 570 , c ) 590 , d ) 610 , e ) 630
Rationale: "the number of seats in the theater is 12 + ( 12 + 2 ) + . . . + ( 12 + 36 ) = 19 ( 12 ) + 2 ( 1 + 2 + . . . + 18 ) = 19 ( 12 ) + 2 ( 18 ) ( 19 ) / 2 = 19 ( 12 + 18 ) = 19 ( 30 ) = 570 the answer is b ."
Answer: b
Python program:
a = 12 + 48 
b = a / 2
c = 48 - 12
d = c + 2 
e = d / 2
f = b * e
Problem: the average age of a family of 6 members is 22 years . if the age of the youngest member is 7 years , what was the average age of the family at the birth of the youngest member ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 12 , e ) 19
Rationale: "present age of total members = 6 x 22 = 132 7 yrs back their ages were = 6 x 7 = 42 ages at the birth of youngest member = 132 - 42 = 90 therefore , avg age at the birth of youngest member = 90 / 6 = 15 . answer : a"
Answer: a
Python program:
a = 6 * 22
b = a - 7
c = b / 4
d = c - 7
Problem: in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.1 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ?
Options: a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 77.12 , e ) 81.6
Rationale: "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.1 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8.1 + 8.5 ) = 24 point of value of the dive = 24.1 * 3.2 = 77.12 answer d"
Answer: d
Python program:
a = 7 + 5 
b = a + 8 
c = b * 3
Problem: calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 20 % and its breadth is decreased by 5 % ?
Options: a ) 14 percent increase
b ) 5 percent increase
c ) 24 percent increase
d ) 13 percent increase
e ) 11 percent increase
Rationale: let l and b be 100 each 100 * 100 = 10000 l increase by 20 % = 120 b decrease by 5 % = 95 120 * 95 = 11400 14 percent increase answer : a
Answer: a
Python program:
a = 100 + 20 
b = 100 - 5
c = a * b
d = 100 * 100
e = c - d
f = 100 * 100
g = e / f
h = g * 100
Problem: how many differently shaped triangles exist in which no two sides are of the same length , each side is of integral unit length and the perimeter of the triangle is less than 14 units ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: explanation : let the lengths of the sides be a , b and c . given , triagle ' s perimeter < 14 = > a + b + c < 14 - - - - - - - - - - ( i ) from triangle inequality theorem , c < a + b = > 2 c < a + b + c . - - - - - - - - - - ( ii ) from ( i ) and ( ii ) , 2 c < a + b + c < 14 . = > c < 7 - - - - - - - - - - ( iii ) = > by similarity , we can say that length of any side must be less than 7 . keeping these in mind , we can find the following possibilities : - ( 2 , 3,4 ) ( 2 , 4,5 ) ( 2 , 5,6 ) ( 3 , 4,5 ) ( 3 , 4,6 ) = > total 5 possibilities . answer : c
Answer: c
Python program:
a = 3 ** 2
b = 14 - a
Problem: a swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side . its volume is ?
Options: a ) 870 m 3 , b ) 277 m 3 , c ) 270 m 3 , d ) 220 m 3 , e ) 170 m 3
Rationale: "volume will be length * breadth * height , but in this case two heights are given so we will take average , volume = ( 12 ∗ 9 ∗ ( 1 + 42 ) ) m 312 ∗ 9 ∗ 2.5 m 3 = 270 m 3 answer : c"
Answer: c
Python program:
a = quadrilateral_area * (
Problem: a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 54 . find the number of notes of rs . 50 denomination .
Options: a ) 15 , b ) 21 , c ) 37 , d ) 19 , e ) 21
Rationale: "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 54 - x now , 50 * x + 500 * ( 54 - x ) = 10350 50 x + 27000 - 500 x = 10350 - 450 x = - 16650 x = 37 . no . of 50 rupees note = 37 . answer : option c"
Answer: c
Python program:
a = 500 * 54
b = a - 10350
c = 500 - 50
d = b / c
Problem: one - third less than 15 % of 180 is equal to :
Options: a ) 18 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "lots of ways to tackle this . 15 % of 180 = 27 1 / 3 of 27 = 9 so , 1 / 3 less than 27 is equal to 27 - 9 = 18 answer : a"
Answer: a
Python program:
a = 15 / 100
b = a * 180
c = 1 / 3
d = 15 / 100
e = d * 180
f = c * e
g = b - f
Problem: evaluate 2.5 / . 0005
Options: a ) 5000 , b ) 500 , c ) 50000 , d ) 50 , e ) 0.5
Rationale: "explanation : 2.5 * 10000 / 5 = 25000 / 5 = 5000 option a"
Answer: a
Python program:
a = 5 / 2
b = 2 / 5
Problem: tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 63000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 10000 , c ) 25000 , d ) 35000 , e ) 30000
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 63000 = 35000 d"
Answer: d
Python program:
a = 2 * 3
b = 2 * a
c = 30000 * b
d = 2 * 3
e = 2 * d
f = e - 2
g = 45000 * f
h = 2 * 3
i = 2 * h
j = 30000 * i
k = g + j 
l = c / k
m = 1 - l
n = 63000 * m
Problem: a wooden cube whose edge length is 5 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 70.6 % , b ) 74.5 % , c ) 78.4 % , d ) 82.1 % , e ) 86.9 %
Rationale: "there are a total of 5 * 5 * 5 = 125 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 3 * 3 * 3 = 27 cubes . the number of cubes with at least one side painted red is 125 - 27 = 98 cubes the probability that a cube has at least one side painted red is 98 / 125 which is 78.4 % the answer is c ."
Answer: c
Python program:
a = 1 * 4
b = volume_cube / (
c = 1 - b
d = 100 * c
Problem: in may mrs lee ' s earnings were 60 percent of the lee family ' s total income . in june mrs lee earned 40 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 64 % , b ) 68 % , c ) 72 % , d ) 76 % , e ) 80 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 60 in may rest of the family ' s income = 40 in june mrs lees income = 60 * 140 / 100 = 84 in june total income = 84 + 40 = 124 % of mrs lee ' s income = 84 / 124 = 67.74 ( b )"
Answer: b
Python program:
a = 100 + 40 
b = 100 + 40 
c = b + 100 
d = a / c
e = d * 100
Problem: if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 86 , how much does one shirt cost ?
Options: a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 24
Rationale: "3 j + 2 s = 69 2 j + 3 s = 86 - - - - - - - - - - - - - - - - 5 j + 5 s = 155 - - - - ( divide by 5 ) - - - > j + s = 31 3 j + 2 s = j + 2 ( j + s ) = j + 62 = 69 - - - > j = 7 3 * 7 + 2 s = 69 21 + 2 s = 69 2 s = 48 s = 24 answer : e"
Answer: e
Python program:
a = 86 * 3
b = 69 * 2
c = a - b
d = 3 * 3
e = 2 * 2
f = d - e
g = c / f
Problem: if the cost price of 17 articles is same as the selling price of 25 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 30 % loss , c ) 32 % loss , d ) 40 % loss , e ) 50 % loss
Rationale: "explanation : 17 cp = 25 sp cost price cp = 25 selling price sp = 17 formula = ( sp - cp ) / cp * 100 = ( 17 - 25 ) / 25 * 100 = 32 % loss answer : option c"
Answer: c
Python program:
a = 100 * 25
b = a / 17
c = 100 - b
d = 100 * 25
e = d / 17
f = c / e
g = 100 * f
Problem: tough and tricky questions : word problems . if bill ' s salary increased by 16 percent , he would earn $ 812 per month . if instead , his salary were to increase by only 10 percent , how much money r would he earn per month ?
Options: a ) $ 700 , b ) $ 754 , c ) $ 770 , d ) $ 782 , e ) $ 893
Rationale: official solution : ( c ) if bill ’ s salary increased by 16 % he would earn $ 812 . algebraically , this can be written as : $ 812 = 1.16 s , where s is his current salary . then s = $ 812 / 1.16 = $ 700 . now that we know his current salary is $ 700 , we can calculate what his salary would be if it were increased by 10 % . we know that 10 % of $ 700 is $ 70 , so his salary would be : r = $ 700 + $ 70 = $ 770 . the correct answer is choice ( c ) .
Answer: c
Python program:
a = 16 / 100
b = 1 + a 
c = 812 / b
d = 10 / 100
e = 1 + d 
f = c * e
Problem: a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 25 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 80 , b ) 28 , c ) 90 , d ) 26 , e ) 11
Rationale: "explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 25 = rs . 80 . answer : a"
Answer: a
Python program:
a = 8925 / 85
b = a - 25
Problem: an aeroplane covers a certain distance of 480 kmph in 4 hours . to cover the same distance in 4 1 / 3 hours , it must travel at a speed of
Options: a ) 440 , b ) 540 , c ) 443 , d ) 740 , e ) 250
Rationale: "speed of aeroplane = 480 kmph distance travelled in 4 hours = 480 * 4 = 1920 km speed of aeroplane to acver 1920 km in 13 / 3 = 1920 * 3 / 13 = 443 km answer c ."
Answer: c
Python program:
a = 480 * 4
b = 3 * 4
c = b + 1 
d = c / 3
e = a / d