euclaise/mathqa_programs huggingface dataset:
Problem: john completes a piece of work in 320 days , rose completes the same work in 480 days . if both of them work together , then the number of days required to complete the work is ?
Options: a ) 190 , b ) 192 , c ) 194 , d ) 196 , e ) 198
Rationale: "if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 320 × 480 / 800 = 192 days answer is b"
Answer: b
Python program:
a = 1 / 320
b = 1 / 480
c = a + b 
d = 1 / c
Problem: in a sports club with 30 members , 18 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 18 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 18 - x ) + ( 19 - x ) + x + 2 = 30 39 - 2 x + x = 30 39 - x = 30 x = 9 so 9 members play both badminton and tennis . c"
Answer: c
Python program:
a = 18 + 19 
b = a + 2 
c = b - 30
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1.2 cm when a man gets on it . the mass of man is
Options: a ) 72 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none
Rationale: "solution volume of water displaced = ( 3 x 2 x 0.012 ) m 3 = 0.072 m 3 . mass of man = volume of water displaced × density of water = ( 0.072 × 1000 ) kg = 72 kg . answer a"
Answer: a
Python program:
a = 3 * 2
b = 1 / 2
c = a * b
d = c * 1000
Problem: what is the probability for a family with 5 children to have two boys and 3 girls ( assuming the probability of having a boy or a girl is equal ) ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 8 , d ) 3 / 16 , e ) 5 / 16
Rationale: one possible case is : girl - girl - girl - boy - boy the probability of this is 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 3 = 10 such cases so we should multiply by 10 . p ( two boys and three girls ) = 10 / 32 = 5 / 16 the answer is e .
Answer: e
Python program:
a = math.factorial(5)
b = math.factorial(3)
c = 5 - 3
d = math.factorial(c)
e = b * d
f = a / e
g = 2 ** 5
h = f / g
Problem: the lowest number which should be added to 5915 so that the sum is exactly divisible by 3 , 5 , 8 and 7 is :
Options: a ) 705 , b ) 825 , c ) 805 , d ) 905 , e ) 810
Rationale: "l . c . m . of 3 , 5 , 8 and 7 = 840 . on dividing 5915 by 840 , the remainder is 35 . number to be added = ( 840 - 35 ) = 805 . answer : option ' c '"
Answer: c
Python program:
a = 5915 / 5
Problem: how many minutes does aditya take to cover a distance of 400 m , if he runs at a speed of 20 km / hr ?
Options: a ) 1 1 / 5 min , b ) 4 1 / 5 min , c ) 3 1 / 5 min , d ) 2 1 / 5 min , e ) none of these
Rationale: explanation : we know that , time = distance / speedspeed = 20 km / hr = 20 x 5 / 18 m / sec = 509 m / sectime = ( 400 x 9 / 50 ) = 72 sec = 1 1 / 5 min answer : a
Answer: a
Python program:
a = 20 * const_0_2778
b = 400 / a
c = b / const_60
Problem: the ratio of sodium chloride to ammonium in 100 kg of mixed ammonium normally used by 3 chemists is 1 : 4 . the amount of sodium chloride to be added to 100 kg of mixed ammonium to make the ratio 9 : 25 is
Options: a ) 5 kg , b ) 6.625 kg , c ) 6.25 kg , d ) 6.35 kg , e ) 8.8 kg
Rationale: sodium chloride in 100 kg = 1 / 5 x 100 = 20 kg ammonium in 100 kg = 4 / 5 x 100 = 80 kg now 80 is 25 parts out of ( 25 + 9 ) = 34 parts . hence 9 parts = 9 / 25 x 80 = 28.8 amount to be added = 28.8 - 20 = 8.8 kg answer : e
Answer: e
Python program:
a = 9 / 25
b = 1 + 4 
c = 4 / b
d = c * 100
e = a * d
f = 1 + 4 
g = 1 / f
h = g * 100
i = e - h
Problem: the salary of a worker is first increased by 30 % and afterwards reduced by 30 % . what is net change in his salary ?
Options: a ) 3 % decrease , b ) 5 % decrease , c ) 9 % decrease , d ) 4 % decrease , e ) 8 % decrease
Rationale: ( 30 * 30 ) / 100 = 9 % decrease answer : c :
Answer: c
Python program:
a = 30 + 100 
b = 30 + 100 
c = b * 30
d = c / 100
e = a - d
f = 100 - e
Problem: think of a number , divide it by 6 and add 5 to it . the result is 17 . what is the number thought of ?
Options: a ) 24 , b ) 72 , c ) 297 , d ) 267 , e ) 29
Rationale: "explanation : 17 - 5 = 12 12 x 6 = 72 answer : b"
Answer: b
Python program:
a = 17 - 5
b = a * 6
Problem: x and y are both integers . if x / y = 57.40 , then what is the sum of all the possible two digit remainders of x / y ?
Options: a ) 560 , b ) 616 , c ) 450 , d ) 900 , e ) 1024
Rationale: "remainder = 0.40 - - > 40 / 100 - - > can be written as ( 40 / 4 ) / ( 100 / 4 ) = 10 / 25 so remainders can be 10 , 20 , 30 , 40 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 = 450 answer : c"
Answer: c
Python program:
a = 3 / 2
b = a * 100
c = 2 + 3 
d = c * 57
e = d + 3 
f = b + e
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12300 after a year ?
Options: a ) 3630 , b ) 3690 , c ) 2887 , d ) 9977 , e ) 2212
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12300 = 3690 . answer : b"
Answer: b
Python program:
a = 6300 + 4200 
b = a + 10500 
c = 6300 / b
d = c * 12300
Problem: $ 406 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?
Options: a ) $ 208 , b ) $ 216 , c ) $ 224 , d ) $ 232 , e ) $ 240
Rationale: let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 406 x = 58 4 x = 232 the answer is d .
Answer: d
Python program:
a = 1 / 2
b = a + 1 
c = b + 2 
d = 406 / c
e = d * 2
Problem: what is the dividend . divisor 18 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 130 , b ) b ) 134 , c ) c ) 148 , d ) d ) 158 , e ) e ) 167
Rationale: "d = d * q + r d = 18 * 9 + 5 d = 162 + 5 d = 167 answer e"
Answer: e
Python program:
a = 18 * 9
b = a + 5
Problem: at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 17 th highest price and the 24 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "there were 16 items sold at a higher price than the radio and 23 items sold at a lower price than the radio . including the radio , there were 16 + 23 + 1 = 40 items sold . the answer is c ."
Answer: c
Python program:
a = 24 + 17 
b = a - 1
Problem: a 15 lt mixture contains water with 20 % of alcohol . if 5 more lts of water added to the mixture what is the percentage of alcohol ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: initially the mixture contains 20 % of 15 = 15 * ( 20 / 100 ) = 3 lts of alcohol after mixing another 5 lts of water . . . the total liquid is 20 lts . . so alcohol percentage = ( 3 / 20 ) * 100 = 15 % answer : b
Answer: b
Python program:
a = 20 / 100
b = a * 15
c = 15 + 5 
d = b / c
e = d * 100
Problem: the average weight of a group of boys is 30 kg . after a boy of weight 35 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 4 , b ) 7 , c ) 6 , d ) 8 , e ) 6
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 35 kg joins the group , total weight of boys = 30 x + 35 so 30 x + 35 + 31 ( x + 1 ) = > x = 4 . answer : a"
Answer: a
Python program:
a = 30 + 1 
b = 35 - a
c = b + 1
Problem: by how much does the larger root of the equation 2 c ^ 2 + 5 c = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: "for 2 c ^ 2 + 5 c = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ."
Answer: e
Python program:
a = 5 ** 2
b = 2 * 12
c = b * 4
d = a + c 
e = math.sqrt(d)
f = 5 + e 
g = 2 * 2
h = f / g
i = 5 ** 2
j = 2 * 12
k = j * 4
l = i + k 
m = math.sqrt(l)
n = 5 - m
o = 2 * 2
p = n / o
q = h - p
Problem: in business , a and c invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by a and b was 3 : 2 , if rs 157300 was their profit , how much amount did b receive .
Options: a ) rs 48000 , b ) rs 47000 , c ) rs 47400 , d ) rs 48400 , e ) none of these
Rationale: "explanation : a : b = 3 : 2 = 6 : 4 = > a : c = 2 : 1 = 6 : 3 = > a : b : c = 6 : 4 : 3 b share = ( 4 / 13 ) * 157300 = 48400 option d"
Answer: d
Python program:
a = 2 + 2 
b = a * 2
c = b * 100
d = c * 100
e = 1 + 2 
f = e + 2 
g = 2 / f
h = d * g
Problem: at a speed of 50 miles per hour , a certain car uses 1 gallon of gasoline every 30 miles . if the car starts with a full 20 gallon tank of gasoline and travels for 5 hours at 50 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 11 / 36 , c ) 5 / 12 , d ) 2 / 3 , e ) 25 / 36
Rationale: "gas used = ( 5 hours ) * ( 50 miles / hour ) * ( 1 gallon / 30 miles ) = 8 + 1 / 3 gallons portion used = ( 8 + 1 / 3 ) / 20 = 5 / 12 ans c"
Answer: c
Python program:
a = 50 * 5
b = a / 30
c = b / 20
Problem: a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 10 more than that received by b , find the total amount shared by a , b and c .
Options: a ) $ 260 , b ) $ 360 , c ) $ 160 , d ) $ 460 , e ) $ 560
Rationale: "a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 10 a = 10 + b ( 1 ) = = = > c = 30 + 3 b - b = 2 b + 30 = = > 2 b - c = - 30 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 10 = 2.5 b - 10 = = > 2.5 b - c = 10 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 40 b = $ 80 a = $ 90 c = 270 - 80 = $ 190 total amount = 90 + 80 + 190 = $ 360 answer : b"
Answer: b
Python program:
a = 3 * 10
b = a * 2
c = 2 * 10
d = b + c 
e = 3 * 10
f = e * 2
g = 2 * 10
h = f + g 
i = h + 10 
j = d + i 
k = 3 * 10
l = k * 2
m = 2 * 10
n = l + m 
o = n + 10 
p = o * 3
q = 3 * 10
r = q * 2
s = 2 * 10
t = r + s 
u = p - t
v = j + u
Problem: in a can , there is a mixture of milk and water in the ratio 5 : 3 . if the can is filled with an additional 20 liters of milk , the can would be full and the ratio of milk and water would become 3 : 1 . find the capacity of the can ?
Options: a ) 52 , b ) 56 , c ) 60 , d ) 64 , e ) 68
Rationale: "let c be the capacity of the can . ( 5 / 8 ) * ( c - 20 ) + 20 = ( 3 / 4 ) * c 5 c - 100 + 160 = 6 c c = 60 the answer is c ."
Answer: c
Python program:
a = 1 * 20
b = 3 * 3
c = 1 * 5
d = b - c
e = a / d
f = e * 5
g = f + 20 
h = 1 * 20
i = 3 * 3
j = 1 * 5
k = i - j
l = h / k
m = l * 3
n = g + m
Problem: when the price of a radio was reduced by 20 % , its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 44 % increase , b ) 44 % decrease , c ) 66 % increase , d ) 75 % increase , e ) none of these
Rationale: let the original price be x and sale be of y units . then , the revenue collected initially = x × y now , new price = 0.8 x , new sale = 1.8 y then , new revenue collected = 1.44 xy % increase in revenue = 0.44 xy / xy × 100 = 44 % increase answer a
Answer: a
Python program:
a = 20 + 20 
b = 20 * 20
c = b / 100
d = a + c
Problem: two trains of length 100 m and 200 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 ) 15 sec , c ) 21 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 + 200 = 300 m . the time required = d / s = 300 / 20 = 15 sec . answer : b"
Answer: b
Python program:
a = 100 + 200 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: the greatest number that exactly divided 105 , 1001 and 2436 is :
Options: a ) 3 , b ) 7 , c ) 11 , d ) 21 , e ) 24
Rationale: solution h . c . f . of 2436 and 1001 is 7 . also , h . c . f . of 105 and 7 is 7 . ∴ h . c . f . of 105 , 1001 and 2436 is 7 . answer b
Answer: b
Python program:
a = 105 / 3
b = 1 + 4 
c = a / b
Problem: how many integers between 324,700 and 478,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,539
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 324,700 and 478,600 is 478,600 - 324,700 = 153,900 - one number per each hundred gives 153,900 / 100 = 1,539 numbers . answer : e ."
Answer: e
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 478 - 600
Problem: a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 37,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 15540
Rationale: "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 37000 × 21 / 50 = 15540 answer is e"
Answer: e
Python program:
a = 5000 * 10
b = 4000 + 5000 
c = b + 5000 
d = a - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 3 * 12
i = h * 1000
j = 5000 * 10
k = i / j
l = g * k
Problem: john would make the 3 - letter codes with 26 alphabets in condition that the middle letter must be vowel and the first letter and the third letter must be different from each other and both are consonant . how many cases of the codes are there ?
Options: a ) 1,980 , b ) 2,020 , c ) 2,100 , d ) 2,200 , e ) 2,500
Rationale: no of vowels : 5 ( a , e , i , o , u ) no of consonants : 21 ( 26 - 5 ) now , the middle letter can be filled up in 5 ways . the first letter can be filled in 21 ways ( as only consonants are allowed ) as one of the consonants is used in the first letter , the third letter can be filled up in 20 ways , so that the letter must be different from each other . so total number of ways = 21 x 5 x 20 = 2100 answer : c
Answer: c
Python program:
a = 2 * 1
Problem: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent . overall he make a . ?
Options: a ) 277 , b ) 209 , c ) 121 , d ) 200 , e ) 128
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 800 = rs . 200 as this is positive , an overall profit of rs . 200 was made . answer : d"
Answer: d
Python program:
a = 4 / 100
b = 1 - a
c = 15000 * b
d = 10 / 100
e = 1 + d 
f = 8000 * e
g = c + f 
h = 15000 + 8000 
i = g - h
Problem: alfred buys an old scooter for $ 4700 and spends $ 800 on its repairs . if he sells the scooter for $ 6000 , his gain percent is ?
Options: a ) 9.1 % , b ) 6.23 % , c ) 7 % , d ) 8.12 % , e ) 10 %
Rationale: "c . p . = 4700 + 800 = $ 5500 s . p . = $ 6000 gain = 6000 - 5500 = $ 500 gain % = 500 / 5500 * 100 = 9.1 % answer is a"
Answer: a
Python program:
a = 4700 + 800 
b = 6000 - a
c = 4700 + 800 
d = b / c
e = d * 100
Problem: what is the sum of all 3 digit nos formed by { 1 , 3,5 , 7,9 } with nos not repeated
Options: a ) 33300 , b ) 34500 , c ) 38500 , d ) 39800 , e ) 45200
Rationale: "here 3 digit no . can be formed in 5 * 4 * 3 = 60 . thus we hv to find the sum of 60 nos . now 60 / 5 = 12 ; we hv 12 no ' s . starting with 1 , 12 no ' s . with 3,5 , 7,9 . . . . so 12 * 100 * ( 1 + 3 + 5 + 7 + 9 ) + 12 * 10 * ( 1 + 3 + 5 + 7 + 9 ) + 12 * 1 * ( 1 + 3 + 5 + 7 + 9 ) = 30000 + 3000 + 300 = 33300 answer : a"
Answer: a
Python program:
a = 1000 - 3
b = 3 * 3
c = b * 10
d = 3 * 3
e = c + d 
f = e + 3 
g = a - f
h = g / 3
i = h + 1 
j = i / 1
k = 1000 - 3
l = 3 * 3
m = l * 10
n = 3 * 3
o = m + n 
p = o + 3 
q = k + p 
r = j * q
Problem: a train 180 m long is running with a speed of 55 km / hr . in what time will it pass a man who is running at 7 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5.5 , b ) 10.45 , c ) 7 , d ) 8 , e ) 9.5
Rationale: "speed of train relative to man = 55 + 7 = 62 km / hr . = 62 * 5 / 18 = 155 / 9 m / sec . time taken to pass the men = 180 * 9 / 155 = 10.45 sec . answer : option b"
Answer: b
Python program:
a = 55 + 7 
b = a * const_0_2778
c = 180 / b
Problem: from a pack of 52 cards , 1 card is drawn at random . find the probability of a face card drawn
Options: a ) 4 / 13 , b ) 1 / 52 , c ) 1 / 4 , d ) 1 / 5 , e ) none of above
Rationale: "explanation : total number of cases = 52 total face cards = 16 [ favourable cases ] so probability = 16 / 52 = 4 / 13 answer : a"
Answer: a
Python program:
a = 4 * 3
b = a / 52
Problem: there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 13,000 after 3 years at the same rate ?
Options: a ) 2372 , b ) 2572 , c ) 4303 , d ) 2343 , e ) 3972
Rationale: let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 13000 . t = 3 years and r = 10 % p . a . c . i . = rs . 13000 x 1 + 10 3 - 1 100 = rs . 13000 x 331 1000 = 4303 . c
Answer: c
Python program:
a = 100 * 100
b = 60 / 6
c = 100 * b
d = c * 3
e = a + d 
f = 60 / 6
g = f / 100
h = 1 + g 
i = 60 / 6
j = i / 100
k = 1 + j 
l = h * k
m = 60 / 6
n = m / 100
o = 1 + n 
p = l * o
q = e * p
r = 100 * 100
s = 60 / 6
t = 100 * s
u = t * 3
v = r + u 
w = q - v
Problem: how many times digit 6 is used while writing numbers from 150 to 1000 ?
Options: a ) 648 , b ) 300 , c ) 252 , d ) 225 , e ) 26
Rationale: "there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 6 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 252 . hence c ."
Answer: c
Python program:
a = 1000 - 150
b = a / 10
c = 10 + 1 
d = 10 + 1 
e = c * d
f = b + e 
g = 6 * 2
h = f + g
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 396 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 396 per week 36 x = 396 x = 11 correct option : a"
Answer: a
Python program:
a = 8 * 3
b = 6 * 2
c = a + b 
d = 396 / c
Problem: 36 men can complete a piece of work in 18 days . in how many days will 54 men complete the same work ?
Options: a ) 24 , b ) 77 , c ) 88 , d ) 29 , e ) 12
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 54 : 36 : : 18 : x x = 12 answer : e ) 12 days"
Answer: e
Python program:
a = 18 * 36
b = a / 54
Problem: ramu bought an old car for rs . 34000 . he spent rs . 12000 on repairs and sold it for rs . 65000 . what is his profit percent ?
Options: a ) 16 % , b ) 17 % , c ) 18 % , d ) 41 % , e ) 13 %
Rationale: "total cp = rs . 34000 + rs . 12000 = rs . 46000 and sp = rs . 65000 profit ( % ) = ( 65000 - 46000 ) / 46000 * 100 = 41 % answer : d"
Answer: d
Python program:
a = 34000 + 12000 
b = 65000 - a
c = 34000 + 12000 
d = b / c
e = d * 100
Problem: john took a bus from home to market , that travels at 50 kmph . while walking back at 5 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 35 kmph . find the average speed .
Options: a ) 8.5 kmph , b ) 16.0 kmph , c ) 22.5 kmph , d ) 18.6 kmph , e ) none of these
Rationale: let the distance be 2 x ( one way ) time taken by bus = 2 x / 50 , by walking = x / 5 , by cycling = x / 35 hours : . average speed = total distance / total time = 5 x / x / 25 + x / 5 + x / 35 = 5 * 60 / 2.4 + 12 + 1.7 = 18.6 answer : d
Answer: d
Python program:
a = 35 / 2
b = const_0_25 + a
Problem: working at a constant rate , p can finish a job in 3 hours . q , also working at a constant rate , can finish the same job in 9 hours . if they work together for 2 hours , how many more minutes will it take p to finish the job , working alone at his constant rate ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "each hour they complete 1 / 3 + 1 / 9 = 4 / 9 of the job . in 2 hours , they complete 2 ( 4 / 9 ) = 8 / 9 of the job . the time for p to finish is ( 1 / 9 ) / ( 1 / 3 ) = ( 1 / 3 ) hour = 20 minutes the answer is a ."
Answer: a
Python program:
a = 1/(3)
b = 1/(9)
c = a + b 
d = c * 2
e = 1 - d
f = 1/(3)
g = e / f
h = g * const_60
Problem: line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 6 ) . what is the slope of line m ?
Options: a ) - 3 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: "ans : b solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 1 ) as we can see that the y axis of intercept point is ( 0 , - 2 ) means line m is parallel to x axis slope m = - 1 ans : b"
Answer: b
Python program:
a = 4 - 6
b = a / 2
c = b + 2 
d = 2 + 6 
e = d / 2
f = c / e
Problem: the average age of a group of persons going for picnic is 16 years . 12 new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is
Options: a ) 5 , b ) 10 , c ) 12 , d ) 40 , e ) 50
Rationale: solution let the initial number of persons be x . then 16 x + 12 x 15 = 15.5 ( x + 20 ) = 0.5 x = 6 x = 12 . answer c
Answer: c
Python program:
a = 15 * 5
b = 12 * 15
c = a - b
d = 16 - 15
e = c / d
Problem: from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 3 hours at 6 kilometers per hour , while ferry q takes a route that is three times longer . if ferry p is slower than ferry q by 3 kilometers per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the distance traveled by ferry p is 18 km . then the distance traveled by ferry q is 54 km . ferry q travels at a speed of 9 kph . the time of the journey for ferry q is 54 / 9 = 6 hours , which is 3 hours more than ferry p . the answer is c ."
Answer: c
Python program:
a = 6 * 3
b = 3 * a
c = 6 + 3 
d = b / c
e = d - 3
Problem: the length of a room is 5 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 21375 , b ) 25750 , c ) 26550 , d ) 26750 , e ) 25725
Rationale: "area = 5 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 5 × 4.75 × 900 = 5 × 4275 = rs . 21375 answer is a ."
Answer: a
Python program:
a = 5 * 4
b = 900 * a