euclaise/mathqa_programs huggingface dataset:
Problem: jim is able to sell a hand - carved statue for $ 670 which was a 25 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 496.30 , b ) $ 536.00 , c ) $ 555.40 , d ) $ 574.90 , e ) $ 588.20
Rationale: "670 = 1.25 * x x = 670 / 1.25 = 536 $ 536 , which is ( b ) ."
Answer: b
Python program:
a = 25 / 100
b = a + 1 
c = 670 / b
Problem: sandy had $ 224 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?
Options: a ) $ 260 , b ) $ 290 , c ) $ 320 , d ) $ 350 , e ) $ 380
Rationale: "let the money sandy took for shopping be x . 0.7 x = 224 x = 320 the answer is c ."
Answer: c
Python program:
a = 100 - 30
b = a / 100
c = 224 / b
Problem: if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 4 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 4
Rationale: "( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 4 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 4 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 4 = e"
Answer: e
Python program:
a = 3 * 1
Problem: each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , forty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 72 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ?
Options: a ) 24 % , b ) 16 % , c ) 11 % , d ) 7 % , e ) 5 %
Rationale: let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.4 i + 0.8 f = 0.72 ( i + f ) 0.08 f = 0.32 i f = 4 i this means that for every 1 incandescent bulb , there are 4 fluorescent bulbs . the percent of bulbs that are switched on which are incandescent is : 0.4 i / ( 0.4 i + 0.8 f ) = 0.4 i / ( 0.4 i + 0.8 * 4 i ) = 0.4 i / 3.6 i = 1 / 9 which is about 11 % . the answer is c .
Answer: c
Python program:
a = 100 - 72
b = 2 / const_0_25
c = b + 2 
d = c * 4
e = a * d
f = e / 100
Problem: a motorcyclist goes from bombay to pune , a distance of 224 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 5 , c ) 4 : 7 , d ) 1 : 1 , e ) 1 : 8
Rationale: "t = 224 / 32 = 7 h t = 7 - 3 = 4 time ratio = 7 : 4 speed ratio = 4 : 7 answer : c"
Answer: c
Python program:
a = 224 / 32
b = 224 / a
c = 224 / 32
d = c - 3
e = 224 / d
f = b / e
Problem: if a is thrice as fast as b and together can do a work in 12 days . in how many days a alone can do the work ?
Options: a ) 16 , b ) 42 , c ) 28 , d ) 54 , e ) 45
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 / 12 = 3 + 1 / 3 x = 4 / 3 x = 1 / 12 x = 12 * 4 / 3 = 16 answer : a"
Answer: a
Python program:
a = 12 * 4
b = 3 / a
c = 1/(b)
Problem: a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 45 km / hr . what is the speed of the car in the second half of the trip ?
Options: a ) 75 , b ) 80 , c ) 90 , d ) 95 , e ) 100
Rationale: "let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 90 + ( d / 2 ) / v d / 180 = d / 2 v and so v = 90 km / hr the answer is c ."
Answer: c
Python program:
a = 45 * 60
b = 45 - 60
c = b * 60
d = a / c
e = 60 * d
f = 60 / 10
g = e / f
Problem: in what ratio p : q should the mixture p of milk and water in the ratio of 5 : 3 be mixed with another mixture q of milk and water in the ratio 1 : 3 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 5 : 2 , b ) 4 : 3 , c ) 3 : 2 , d ) 2 : 1 , e ) 4 : 1
Rationale: "( 5 / 8 ) * p + ( 1 / 4 ) * q = ( 3 / 8 ) * p + ( 3 / 4 ) * q 2 p = 4 q p / q = 2 / 1 the answer is d ."
Answer: d
Python program:
a = 4 + 0 
b = 5 + 1 
c = a - b
d = c + 1
Problem: a person travels from p to q a speed of 80 km / hr and returns by increasing his speed by 10 % . what is his average speed for both the trips ?
Options: a ) 33 , b ) 77 , c ) 48 , d ) 84 , e ) 21
Rationale: "speed on return trip = 110 % of 80 = 88 km / hr . average speed of trip = 80 + 88 / 2 = 168 / 2 = 84 km / hr answer : d"
Answer: d
Python program:
a = 10 / 100
b = 1 + a 
c = 80 * b
d = c + 80 
e = d / 2
Problem: a tempo is insured to an extent of 4 / 5 of its original value . if the premium on it at the rate of 1.3 % amounts to $ 910 , the original value of the tempo is ?
Options: a ) 92500 , b ) 75230 , c ) 65990 , d ) 45280 , e ) 87500
Rationale: let the original value of the tempo is $ x 1.3 % of 4 / 5 of x = 910 ( 13 / 10 ) * ( 1 / 100 ) * ( 4 / 5 ) x = 910 x = $ 87500 answer is e
Answer: e
Python program:
a = 4 / 5
b = a * 1
c = b / 100
d = 910 / c
Problem: a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 60 meters , what is the height of the building ( in meters ) ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: the height : length ratio will be equal in both cases . 18 / 45 = x / 60 x = 24 the answer is b .
Answer: b
Python program:
a = 18 / 45
b = 60 * a
Problem: fresh grapes contain 70 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 30 kgs of raisins ?
Options: a ) 75 kgs , b ) 64 kgs , c ) 72 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: "the weight of non - water in 30 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 70 = 30 % of whole weight ) , so 30 * 0.75 = x * 0.3 - - > x = 75 . answer : a ."
Answer: a
Python program:
a = 100 - 25
b = 30 * a
c = b / 100
d = c + 70
Problem: in a class of 38 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 15
Rationale: "total # of students = 38 avg # of books per student = 2 total # of books = 38 * 2 = 76 # of student borrowed at least 3 books = 38 - 2 - 12 - 10 = 14 # of books borrowed by above 14 students = 76 - ( 12 * 1 ) + ( 10 * 2 ) = 44 considering that 13 out of above 14 students borrowed only 3 books , # of books borrowed = 13 * 3 = 39 so maximum # of books borrowed by any single student = 44 - 39 = 5 option b"
Answer: b
Python program:
a = 38 * 2
b = 12 * 1
c = b + 10 
d = c + 2 
e = 38 - d
f = e - 1
g = f * 3
h = 12 * 1
i = 10 * 2
j = h + i 
k = g + j 
l = a - k
Problem: in a hostel there were 100 students . to accommodate 25 more students the average is decreased by some rupees . but total expenditure increased by rs . 500 . if the total expenditure of the hostel now 8500 , find decrease of average budget ?
Options: a ) 20 , b ) 15 , c ) 12 , d ) 18 , e ) 24
Rationale: "let average is x 100 x + 500 = 8500 x = 80 let decrease = y 125 ( 80 – y ) = 8500 y = 12 answer : c"
Answer: c
Python program:
a = 100 + 25 
b = a * 500
c = b + 8500 
d = c / 25
e = d - 500
f = 100 + 25 
g = e * f
Problem: 8 men , working 7 hours a day can complete a work in 18 days . how many hours a day must 12 men work to complete the same work in 12 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the number of hours required to complete the work is 8 * 7 * 18 = 1008 12 × 12 × ( x ) = 1008 x = 7 the answer is b ."
Answer: b
Python program:
a = 8 * 7
b = a * 18
c = 12 * 12
d = b / c
Problem: of the four - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 6048 , b ) 3648 , c ) 7248 , d ) 1448 , e ) 2168
Rationale: "of the four - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for p - 9 ways ; choosing the digit for q - 8 ways ; choosing the digit for r - 7 ways ; # of permutations of 3 digits in ppqr - 4 ! / 2 ! total : 9 * 8 * 7 * 4 ! / 2 ! = 6048 . answer : a ."
Answer: a
Python program:
a = 10 - 1
b = 10 - 2
c = a * b
d = c * 1
Problem: ( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ?
Options: a ) 420 , b ) 260 , c ) 200 , d ) 300 , e ) 400
Rationale: explanation : ( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 × 5 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 ) 0.75 × ( 5 ) 0.75 = ( 5 ) ( 1.25 + 0.75 ) × ( 12 ) ( 0.25 + 0.75 ) = ( 5 ) 2 × ( 12 ) 1 = 25 × 12 = 300 answer : option d
Answer: d
Python program:
a = 60 ** 0
b = 5 ** 1
c = 12 ** 0
d = b * c
e = a * d
Problem: a computer factory produces 4200 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 , b ) 3.125 . , c ) 4.5 , d ) 5.225 , e ) 6.25
Rationale: "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 4200 / ( 28 * 24 * 2 ) = 3.125 answer b"
Answer: b
Python program:
a = 4200 / 28
b = 28 - 4
c = b * 2
d = a / c
Problem: a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is 12 , what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 2 and 6 , d ) 4 , e ) can not be determined .
Rationale: "a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 4 - - > x ^ 2 + 4 x = 4 i . e x ^ 2 + 4 x - 12 = 0 is the quadratic equation which needs to be solved . ( x - 2 ) ( x + 6 ) = 0 hence x = 2 , x = - 6 imo c"
Answer: c
Python program:
a = 12 ** 2
b = a / 4
Problem: a bowl of fruit contains 14 apples and 20 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: "number of apples = 14 number of oranges = 20 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 20 - x ) = 34 - x 14 / ( 34 - x ) = 7 / 10 = > 20 = 34 - x = > x = 14 answer c"
Answer: c
Python program:
a = 14 + 20 
b = 70 / 100
c = a * b
d = c - 14
e = 70 / 100
f = d / e
Problem: the area of a square field is 1225 km 2 . how long will it take for a horse to run around at the speed of 20 km / h ?
Options: a ) 7 h , b ) 10 h , c ) 8 h , d ) 6 h , e ) none of these
Rationale: explanation area of field = 1225 km 2 . then , each side of field = √ 1225 = 35 km distance covered by the horse = perimeter of square field = 35 × 4 = 140 km ∴ time taken by horse = distances / peed = 140 / 20 = 7 h answer a
Answer: a
Python program:
a = math.sqrt(1225)
b = 4 * a
c = b / 20
Problem: xavier starts from p towards q at a speed of 50 kmph and after every 12 mins increases his speed by 10 kmph . if the distance between p and q is 52 km , then how much time does he take to cover the distance ?
Options: a ) 40 , b ) 60 , c ) 48 , d ) 70 , e ) 80
Rationale: first 12 min = 50 * 12 / 60 = 10 km 2 nd 12 min = 60 * 12 / 60 = 12 km 3 rd 12 min = 70 * 12 / 60 = 14 km 4 th 12 min = 80 * 12 / 60 = 16 km total time 12.4 = 48 min c
Answer: c
Python program:
a = 12 + 12 
b = a + 12 
c = b + 12
Problem: a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 5 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 89.0 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 5 % of 400 = 20 therefore , total number of rotten fruits = 90 + 20 = 110 therefore number of fruits in good condition = 1000 - 110 = 890 therefore percentage of fruits in good condition = ( 890 / 1000 × 100 ) % = ( 89000 / 1000 ) % = 89.0 % answer : b"
Answer: b
Python program:
a = 600 + 400 
b = 15 / 100
c = 600 * b
d = 5 / 100
e = 400 * d
f = c + e 
g = a - f
h = 600 + 400 
i = g / h
j = i * 100
Problem: if a rectangular room measures 8 meters by 5 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters )
Options: a ) 24,000
b ) 16 , 000,000
c ) 2 , 400,000
d ) 24 , 000,000
e ) 240 , 000,000
Rationale: b . 160 , 000,000 8 * 100 * 5 * 100 * 4 * 100 = 160 , 000,000
Answer: b
Python program:
a = 4 * 100
b = 1 / 10
c = a * b
d = 5 * 100
e = c * d
f = 8 * 100
g = e * f
Problem: on a 20 mile course , pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break , ran the rest of the distance at an average rate of 8 miles per hour . how many minutes did pat take to cover the entire course ?
Options: a ) 75 , b ) 105 , c ) 117 , d ) 150 , e ) 162
Rationale: at an average rate of 30 miles per hour in 12 minute ( 1 / 5 hours ) pat covers ( distance ) = ( time ) * ( rate ) = 1 / 5 * 30 = 6 miles , thus she should cover the remaining distance of 20 - 6 = 14 miles at an average rate of 8 miles per hour . to cover 14 miles at an average rate of 8 miles per hour pat needs ( time ) = ( distance ) / ( rate ) = 14 / 8 = 1.75 hours = 105 minutes . therefore pat needs total of 12 + 105 = 117 minutes to cover the entire course . answer : c .
Answer: c
Python program:
a = 12 / const_60
b = 30 * a
c = 20 - b
d = c / 8
e = d * const_60
f = e + 12
Problem: the sum of all the integers k such that – 25 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 47
Rationale: "- 24 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 24 - 23 sum of which is - 47 . hence option d . e"
Answer: e
Python program:
a = negate + ( 
b = a + 1
Problem: sonika deposited rs . 14500 which amounted to rs . 12200 after 3 years at simple interest . had the interest been 3 % more . she would get how much ?
Options: a ) 13505 , b ) 12004 , c ) 15003 , d ) 14500 , e ) 16400
Rationale: "( 14500 * 3 * 3 ) / 100 = 1305 12200 - - - - - - - - 13505 answer : a"
Answer: a
Python program:
a = 3 / 100
b = 12200 - 14500
c = b / 3
d = c / 14500
e = a + d 
f = e * 14500
g = f * 3
h = g + 14500
Problem: the sale price sarees listed for rs . 298 after successive discount is 12 % and 15 % is ?
Options: a ) 321 , b ) 223 , c ) 245 , d ) 265 , e ) 162
Rationale: "explanation : 298 * ( 88 / 100 ) * ( 85 / 100 ) = 223 answer : b"
Answer: b
Python program:
a = 298 * 12
b = a / 100
c = 298 - b
d = 298 * 12
e = d / 100
f = 298 - e
g = f * 15
h = g / 100
i = c - h
Problem: 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 170 kg then find the average weight of all the 7 rounds ?
Options: a ) 97.1 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 170 / 7 = 97.1 kgs answer : a"
Answer: a
Python program:
a = 1 + 3 
b = a * 170
c = b / 7
Problem: if the area of the equilateral triangle above is 0.75 , what is the area of the adjacent square ?
Options: a ) ( √ 3 ) / 2
b ) √ 3
c ) √ 6
d ) 3
e ) 2 √ 3
Rationale: area of equilateral triangle : a ^ 2 * ( square root of 3 ) / 4 = 0.75 hence , area of square = a ^ 2 = 0.75 * 4 / ( square root of 3 ) = 3 / ( square root of 3 ) = square root of 3 answer : b
Answer: b
Python program:
a = 0 * 75
b = math.sqrt(3)
c = a / b
Problem: a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 20 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 60 , b ) 50 , c ) 40 , d ) 70 , e ) 45
Rationale: "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 20 % of 50 % i . e 10 % . so he completed 50 + 10 = 60 % of total trip a"
Answer: a
Python program:
a = 100 / 2
b = 100 / 2
c = 20 * b
d = c / 100
e = a + d
Problem: it has been raining at the rate of 5 centimeters per hour . if the rain filled a cylindrical drum with a depth of 15 centimeters , and area 300 square centimeters , how long did it take to fill the drum completely ?
Options: a ) 3 hours
b ) 4 hours 15 minutes
c ) 6 hours
d ) 2 hours 5 minutes
e ) 8 hours
Rationale: answer is : a , 3 hours the volume of the drum is irrelevant and only height matters since rain fell all over the city . thus , it takes only 15 / 5 = 3 hours of rain to fill the drum
Answer: a
Python program:
a = 15 / 5
Problem: in digging a pond 28 m * 10 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 3387 , b ) 1000 , c ) 2866 , d ) 2787 , e ) 1400
Rationale: "28 * 10 * 5 = 1400 answer : e"
Answer: e
Python program:
a = 28 * 10
b = a * 5
Problem: suppose you work for a manufacturing plant that pays you $ 12.50 an hour and $ . 16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 800 ( before payroll deductions ) ?
Options: a ) 1800 , b ) 1825 , c ) 1850 , d ) 1855 , e ) 1875
Rationale: "hourly = $ 12.50 / hour totalhours = 40 piecework = $ 0.16 / widget totalpieces = ? ? ? ? total pay = ( hourly * totalhours ) + ( piecework * totalpieces ) so , put it all together : $ 800 = ( $ 12.50 * 40 ) + ( $ 0.16 * total pieces ) totalpieces = ( $ 800 - ( $ 12.50 * 40 ) ) / $ 0.16 = 1875 widgets e . 1875"
Answer: e
Python program:
a = 12 * 50
b = 800 - a
c = b / 16
Problem: the diameter of a cylindrical tin is 10 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 125 , b ) 155 , c ) 130 , d ) 120 , e ) 100
Rationale: "r = 5 h = 5 π * 5 * 5 * 5 = 125 π cc answer : a"
Answer: a
Python program:
a = 10 / 2
b = volume_cylinder / (
Problem: if 8 spiders make 4 webs in 9 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 10 , b ) 20 , c ) 12 , d ) 16 , e ) 18
Rationale: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 8 : 1 ( webs ) 1 : 9 } : : x : 4 â ‡ ’ 8 ã — 1 ã — 9 = 1 ã — 4 ã — x â ‡ ’ x = 18 answer : option e"
Answer: e
Python program:
a = 1 * 8
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 9 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 79
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 9 ^ 2 - 2 = 79 . thus , the answer is e ."
Answer: e
Python program:
a = 2 ** 2
b = a - 2
Problem: ( 150 % of 1265 ) ÷ 7 = ?
Options: a ) a ) 125 , b ) b ) 175 , c ) c ) 271 , d ) d ) 375 , e ) e ) 524
Rationale: "explanation : ? = ( 150 x 1265 / 100 ) ÷ 7 = 189750 / 700 = 271 answer : option c"
Answer: c
Python program:
a = 150 / 100
b = a * 1265
c = b / 7
Problem: two vessels contains equal number of mixtures milk and water in the ratio 7 : 2 and 8 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 1 , d ) 11 : 3 , e ) 15 : 4
Rationale: "the ratio of milk and water in the new vessel is = ( 7 / 9 + 8 / 9 ) : ( 2 / 9 + 1 / 9 ) = 15 / 9 : 3 / 9 = 5 : 1 answer is c"
Answer: c
Python program:
a = 8 + 1 
b = 7 + 2 
c = a / b
d = 7 * c
e = d + 8 
f = 8 + 1 
g = 7 + 2 
h = f / g
i = 2 * h
j = i + 1 
k = e / j
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 12 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 477 , b ) 396 , c ) 279 , d ) 276 , e ) 291
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 12 + 21 = 33 t = 12 d = 33 * 12 = 396 . answer : b"
Answer: b
Python program:
a = 21 - 12
b = 60 / a
c = b * 12
d = 21 - 12
e = 60 / d
f = e * 21
g = c + f
Problem: a part of certain sum of money is invested at 9 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 7 , b ) 4 : 0 , c ) 4 : 3 , d ) 4 : 1 , e ) 4 : 2
Rationale: "12 : 9 = 4 : 3 answer : c"
Answer: c
Python program:
a = 12 / 100
b = a * 9
Problem: the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 58 , then 1 / m + 1 / n is equal to
Options: a ) 1 / 35 , b ) 3 / 35 , c ) 5 / 37 , d ) 2 / 35 , e ) none
Rationale: "answer we have , m x n = 6 x 210 = 1260 â ˆ ´ 1 / m + 1 / n = ( m + n ) / mn = 58 / 1260 = 17 / 620 correct option : e"
Answer: e
Python program:
a = 6 * 210
b = 58 / a
Problem: a 30 kg metal bar made of alloy of tin and silver lost 3 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 3 kg when 30 kg alloy is immersed . this is a loss of ( 3 / 30 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"
Answer: e
Python program:
a = 0 / 375
b = a * 30
c = 3 - b
d = 1 / 375
e = 0 / 375
f = d - e
g = c / f
h = 0 / 375
i = h * 30
j = 3 - i
k = 1 / 375
l = 0 / 375
m = k - l
n = j / m
o = 30 - n
p = g / o
Problem: the diameter of a cylindrical tin is 14 cm and height is 2 cm . find the volume of the cylinder ?
Options: a ) 33 , b ) 45 , c ) 66 , d ) 77 , e ) 98
Rationale: "r = 7 h = 5 π * 7 * 7 * 5 = 98 π cc answer : e"
Answer: e
Python program:
a = 14 / 2
b = volume_cylinder / (
Problem: a shopkeeper sold an article for rs 2552.36 . approximately what was his profit percent if the cost price of the article was rs 2400
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: explanation : gain % = ( 152.36 * 100 / 2400 ) = 6.34 % = 6 % approx option c
Answer: c
Python program:
a = 2552 - 36
b = a / 2400
c = 100 * b
d = math.floor(c)
Problem: the balance of a trader weighs 10 % less than it should . still the trader marks up his goods to get an overall profit of 30 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 8 % , c ) 25 % , d ) 17 % , e ) 9 %
Rationale: "the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 90 gms because it weighs 10 % less . say , the cost price is $ 90 ( $ 1 / gm ) . since he gets a profit of 30 % , the selling price must be 90 + ( 30 / 100 ) * 90 = $ 117 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 117 , the mark up is simply 17 % . ans : d"
Answer: d
Python program:
a = 4 * 10
b = 30 / 100
c = a * b
d = 4 * 10
e = c + d 
f = e - 100