euclaise/mathqa_programs huggingface dataset:
Problem: a fruit drink is made of orange , watermelon , and grape juice , where 25 percent of the drink is orange juice and 40 percent is watermelon juice . if the drink is made with 70 ounces of grape juice , how many ounces is the drink total ?
Options: a ) 125 , b ) 160 , c ) 200 , d ) 250 , e ) 320
Rationale: "let the total number of ounces in the drink be x . % of orange = 25 % % of watermelon = 40 % % of grape = 100 % - 65 % = 35 % 0.35 x = 70 x = 200 therefore there are a total of 200 ounces in the drink . the answer is c ."
Answer: c
Python program:
a = 70 * 25
b = 40 + 25 
c = 100 - b
d = a / c
e = 70 + d 
f = 70 * 40
g = 40 + 25 
h = 100 - g
i = f / h
j = e + i
Problem: the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
Options: a ) 18.75 % , b ) 23 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: let wage of erica = 10 wage of robin = 1.3 * 10 = 13 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 13 ) / 13 * 100 % = 3 / 13 * 100 % = 23 % answer b
Answer: b
Python program:
a = 100 + 60 
b = 100 + 30 
c = a - b
d = 100 + 30 
e = c / d
f = e * 100
Problem: find the surface area of a cuboid 12 m long , 14 m broad and 7 m high
Options: a ) 868 sq . cm
b ) 600 sq . cm
c ) 700 sq . cm
d ) 900 sq . cm
e ) none of these
Rationale: explanation : surface area = [ 2 ( 12 x 14 + 14 x 7 + 12 x 7 ) ] cm 2 = ( 2 x 350 ) cm 2 = 700 cm 2 . answer : c
Answer: c
Python program:
a = 12 * 14
b = 12 * 7
c = a + b 
d = 14 * 7
e = c + d 
f = 2 * e
Problem: the speed of a boat in still water in 42 km / hr and the rate of current is 7 km / hr . the distance travelled downstream in 44 minutes is :
Options: a ) 86.6 km , b ) 46.6 km , c ) 35.9 km , d ) 35.6 km , e ) 26.6 km
Rationale: "speed downstream = ( 42 + 7 ) = 49 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 49 = 35.9 km answer : c"
Answer: c
Python program:
a = 42 + 7 
b = 44 / const_60
c = a * b
Problem: the sum of ages of 5 children born at the intervals of 3 years each is 60 years . what is the age of the youngest child ?
Options: a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 60 5 x = 30 x = 6 . age of the youngest child = x = 6 years . c )"
Answer: c
Python program:
a = 60 / 5
b = a - 3
c = b - 3
Problem: a 100 - litre mixture of milk and water contains 36 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 9 % . what is the value of x ?
Options: a ) 57.5 litres , b ) 56.67 litres , c ) 57.67 litres , d ) 56.5 litres , e ) 50 litres
Rationale: "working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 36 % ( 1 - x / 100 ) ^ 2 = 9 % * 100 % ( 1 - x / 100 ) ^ 2 = 9 / 36 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 3 / 6 ) ^ 2 100 - x = 300 / 6 x = 50 ans e"
Answer: e
Python program:
a = 9 / 36
b = math.sqrt(a)
c = 1 - b
d = 100 * c
Problem: the length of each side of an equilateral triangle having an area of 4 √ 3 cm 2 is ?
Options: a ) 3 : 4
b ) 3 : 9
c ) 3 : 7
d ) 3 : 1
e ) 3 : 2
Rationale: let the speed of the train be x km / hr and that of the car be y km / hr . then , 120 / x + 480 / y = 8 or 1 / x + 4 / y = 1 / 15 - - - ( i ) and , 200 / x + 400 / y = 25 / 3 or 1 / x + 2 / y = 1 / 24 - - - ( ii ) solving ( i ) and ( ii ) , we get x = 60 and y = 80 ratio of speeds = 60 : 80 = 3 : 4 answer : a
Answer: a
Python program:
a = 3 / 4
Problem: length of a rectangular plot is 24 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 52 m , b ) 62 m , c ) 72 m , d ) 82 m , e ) 92 m
Rationale: "let breadth = x metres . then , length = ( x + 24 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 24 ) + x ] = 200 2 x + 24 = 100 2 x = 76 x = 38 . hence , length = x + 24 = 62 m b"
Answer: b
Python program:
a = 5300 / 26
b = 2 * 24
c = a + b 
d = c / 4
Problem: if x is real , find the maximum value of the expression - 2 x ^ 2 + 7 x + 9 .
Options: a ) 6.125 , b ) 9.125 , c ) 12.125 , d ) 15.125 , e ) 18.125
Rationale: "this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 7 x + 9 = ( - 2 x + 9 ) ( x + 1 ) the roots are 9 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 1.75 the maximum value is - 2 ( 1.75 ) ^ 2 + 7 ( 1.75 ) + 9 = 15.125 the answer is d ."
Answer: d
Python program:
a = 2 * 2
b = a / 7
c = 7 * b
d = c + 9 
e = 2 * 2
f = e / 7
g = f ** 2
h = 2 * g
i = d - h
Problem: the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 150 . what is the manager ' s monthly salary ?
Options: a ) rs . 6003 , b ) rs . 6029 , c ) rs . 4650 , d ) rs . 6108 , e ) rs . 6011
Rationale: "explanation : manager ' s monthly salary rs . ( 1650 * 21 - 1500 * 20 ) = rs . 4650 . answer : c"
Answer: c
Python program:
a = 1500 + 150 
b = 20 + 1 
c = a * b
d = 1500 * 20
e = c - d
Problem: the probability of two events a and b are 0.25 and 0.30 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
Options: a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6
Rationale: we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 30 - . 15 = . 40 but the probability of neither a nor b = 1 - . 40 = 0.60 answer : e
Answer: e
Python program:
a = 0 + 25 
b = a - 0
c = 1 - b
Problem: the size of a flat - screen tablet is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 6 - inch flat - screen tablet than a square 5 - inch flat - screen tablet ?
Options: a ) 5.0
b ) 6.0
c ) 6.8
d ) 5.8
e ) 5.5
Rationale: if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 6 - inch flat - screen television the diagonal ( hypotenuse ) = 6 so , we can apply the pythagorean theorem to get x ² + x ² = 6 ² simplify : 2 x ² = 6 ² divide both sides by 2 to get : x ² = 6 ² / 2 since the area of the square = x ² , we can see that the area of this square is 6 ² / 2 square 5 - inch flat - screen television the diagonal ( hypotenuse ) = 5 so , we can apply the pythagorean theorem to get x ² + x ² = 5 ² simplify : 2 x ² = 5 ² divide both sides by 2 to get : x ² = 5 ² / 2 since the area of the square = x ² , we can see that the area of this square is 5 ² / 2 difference in areas = 6 ² / 2 - 5 ² / 2 = ( 6 ² - 5 ² ) / 2 = ( 36 - 25 ) / 2 = 11 / 2 = 5.5 e
Answer: e
Python program:
a = 6 ** 2
b = a / 2
c = 5 ** 2
d = c / 2
e = b - d
Problem: the sum of 4 consecutive even numbers is 140 . what would be the largest number ?
Options: a ) 33 , b ) 38 , c ) 70 , d ) 123 , e ) 12
Rationale: let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x + 1 ) = 38 . answer : b
Answer: b
Python program:
a = 140 - 12
b = a / 4
c = b + 2 
d = c + 2 
e = d + 2
Problem: in a sample of college students , 50 percent are third year students and 70 percent are not second - year students . what fraction of those students who are not third - year students are second - year students ?
Options: a ) 2 / 3 , b ) 1 / 4 , c ) 2 / 5 , d ) 3 / 7 , e ) 2 / 9
Rationale: required answer = 40 / 60 . = 2 / 3 answer is a
Answer: a
Python program:
a = 100 - 50
b = 3 * 10
c = a - b
d = 3 * 10
e = c / d
Problem: a camera lens filter kit containing 5 filters sells for $ 75.50 . if the filters are purchased individually , 3 of them are priced at $ 7.35 each , 3 at $ 12.05 each , 1 at $ 12.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 5.35 % , b ) 6.35 % , c ) 7.35 % , d ) 8.35 % , e ) 9.35 %
Rationale: "cost of kit = $ 75.50 if filters are purchased individually - $ 7.35 * 3 + $ 12.05 * 3 + $ 12.50 = $ 70.70 amount saved = $ 75.50 - $ 70.70 = $ 4.80 required % age = ( $ 4.80 / $ 75.50 ) * 100 = 6.35 % so , the correct answer is b ."
Answer: b
Python program:
a = 3 * 7
b = 3 * 12
c = a + b 
d = 12 + 50 
e = 75 - 50
f = e * 100
g = f / 75
Problem: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability e that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability e = 1 / 24 . answer c ."
Answer: c
Python program:
a = 20 + 4 
b = 1 / a
Problem: when positive integer n is divided by positive integer j , the remainder is 16 . if n / j = 204.04 , what is value of j ?
Options: a ) 100 , b ) 120 , c ) 400 , d ) 260 , e ) 380
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.04 here 204 is the quotient . given that remainder = 16 so , 204.04 = 204 + 16 / j so , j = 400 answer : c"
Answer: c
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 204 - 4
e = 16 / d
Problem: find the lowest common multiple of 24 , 36 and 40 .
Options: a ) 360 , b ) 420 , c ) 510 , d ) 320 , e ) 280
Rationale: "lcm = 2 * 2 * 2 * 3 * 3 * 5 = 360 . answer is a"
Answer: a
Python program:
a = math.lcm(24, 36)
b = math.lcm(a, 40)
Problem: 14 is what percent of 70 ?
Options: a ) 0.2 % , b ) 2 % , c ) 5 % , d ) 20 % , e ) 500 %
Rationale: "14 = x * 70 / 100 x = 20 % ans ; d"
Answer: d
Python program:
a = 14 / 70
b = a * 100
Problem: the perimeter of a semi circle is 140 cm then the radius is ?
Options: a ) 27 , b ) 28 , c ) 19 , d ) 11 , e ) 12
Rationale: "36 / 7 r = 140 = > r = 27 answer : a"
Answer: a
Python program:
a = 2 + math.pi 
b = 140 / a
Problem: among the members of the malmo family , there are 3 times as many members who do not wear glasses as members who do . half of the malmo family members have blue eyes , and 4 / 5 of the family members who have blue eyes do not wear glasses . what percent of the malmo family members wear glasses and do not have blue eyes ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 35
Rationale: number in black are given and in red are calculated . now , since x + 3 x = 100 , then x = 25 and therefore = 25 − 10 = 15 answer : b .
Answer: b
Python program:
a = 3 / 5
b = a / 4
c = b * 100
Problem: a train passes a station platform in 20 sec and a man standing on the platform in 12 sec . if the speed of the train is 72 km / hr . what is the length of the platform ?
Options: a ) 227 , b ) 140 , c ) 160 , d ) 120 , e ) 171
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . length of the train = 20 * 12 = 240 m . let the length of the platform be x m . then , ( x + 240 ) / 20 = 20 = > x = 160 m . answer : c"
Answer: c
Python program:
a = 72 * const_0_2778
b = 12 * a
Problem: the distance between two cities a and b is 870 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 pm , b ) 07 pm , c ) 03 pm , d ) 05 am , e ) 03 am
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 870 . therefore , 60 x + 75 ( x - 1 ) = 870 . = > x = 7 . so , they meet at ( 8 + 7 ) i . e , 15 = > 3 pm answer : c )"
Answer: c
Python program:
a = 870 + 75 
b = 60 + 75 
c = a / b
d = c + 8
Problem: apple , orange , mango . mango + apple = 12 . mango + orange = 10 . mango + apple + orange = 38 . calculate the no of mango ?
Options: a ) - 8 , b ) - 9 , c ) - 10 , d ) - 12 , e ) - 16
Rationale: mango + apple = 12 . . . . . . . . . . . . . ( a ) mango + orange = 10 . . . . . . . . . . ( b ) adding a and b 2 mango + apple + orange = 22 but mango + apple + orange = 38 . . . . given which is not possible . in this case , no of mangoes is negative ( - 16 ) answer : d
Answer: d
Python program:
a = 38 - 12
b = 10 - a
Problem: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 360 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 110 , c ) 120 , d ) 140 , e ) 220
Rationale: "orchestra seats - a balcony seats - b a + b = 360 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 360 = 3320 - 2880 = 440 i . e . a = 110 and b = 360 - 110 = 250 more seats in balcony than orchestra = b - a = 250 - 110 = 140 answer : option d"
Answer: d
Python program:
a = 12 * 360
b = 3 * 1000
c = 3 * 100
d = b + c 
e = 2 * 10
f = d + e 
g = a - f
h = 12 - 8
i = g / h
j = 12 * 360
k = 3 * 1000
l = 3 * 100
m = k + l 
n = 2 * 10
o = m + n 
p = j - o
q = 12 - 8
r = p / q
s = 360 - r
t = i - s
Problem: a train running at the speed of 36 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 180 metres , c ) 324 metres , d ) 90 metres , e ) 100 meters
Rationale: "speed = 36 x 5 / 18 m / sec = 30 / 3 m / sec . length of the train = ( speed x time ) . length of the train = 30 / 3 x 9 m = 90 m . answer : d"
Answer: d
Python program:
a = 36 * 1000
b = a / 3600
c = b * 9
Problem: tough and tricky questions : arithmetic . ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 =
Options: a ) 4 , b ) 18 , c ) 29 , d ) 8 , e ) 116
Rationale: ans is 8 my approach was : ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 = 56 ( 56 + 56 ) / 28 * 28 = 56 * 112 / 28 * 28 = 2 * 4 = 8 d
Answer: d
Python program:
a = 56 ** 2
b = 56 ** 2
c = a + b 
d = 28 ** 2
e = c / d
Problem: a boy has rs . 480 in the denominations of one - rupee notes , 5 - rupee notes and 10 - rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ?
Options: a ) 90 , b ) 110 , c ) 140 , d ) 130 , e ) 120
Rationale: let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 . a
Answer: a
Python program:
a = 4 * 4
b = 480 / a
c = b * 3
Problem: glen and hannah drive at constant speeds toward each other on a highway . glen drives at a constant speed of 37 km per hour . at a certain time they pass by each other , and then keep driving away from each other , maintaining their constant speeds . if glen is 130 km away from hannah at 6 am , and also 130 km away from hannah at 11 am , then how fast is hannah driving ( in kilometers per hour ) ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: glen and hannah complete 260 km / 5 hours = 52 km / hour hannah ' s speed is 52 - 37 = 15 km / hour the answer is d .
Answer: d
Python program:
a = 130 * 2
b = 11 - 6
c = a / b
d = c - 37
Problem: the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 20 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: "let initial output is o then after 10 % increase it will be 1.1 o and after 20 % increase on this new output the latest output will be 1.1 o * 1.20 = 1.32 o now we have to decrease the output by some percentage so that the new output is same as the starting output ( o ) so , 1.32 o * ( 1 - x / 100 ) = o = > x = 24.24 % so , answer will be b"
Answer: b
Python program:
a = 100 + 10 
b = 100 + 10 
c = 20 / 100
d = b * c
e = a + d 
f = e - 100
g = f * 100
h = 100 + 10 
i = 100 + 10 
j = 20 / 100
k = i * j
l = h + k 
m = g / l
Problem: integer d is the product of the integers a , b , and c and 1 < a < b < c . if the remainder when 233 is divided by d is 79 , what is the value of a + c ?
Options: a ) 7 , b ) 9 , c ) 13 , d ) 14 , e ) 18
Rationale: 79 is the remainder , therefore the number ( a * b * c ) or multiple of the number we need is 79 less than 233 hence 233 - 79 = 154 therefore , 154 is either a number we want or it is a multiple of the number we want but the largest factor of 154 is 77 because 77 * 2 = 154 but 77 is less than 79 hence it can not be a number thus 154 is the number we want a * b * c = 154 now factorize 154 = 1 * 2 * 7 * 11 all are prime also we know 1 < a < b < c thus a = 2 and c = 11 therefore a + c = 2 + 11 = 13 answer : c
Answer: c
Python program:
a = 233 - 79
b = a / 2
c = 3 + 4 
d = b / c
e = 2 + d
Problem: each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 15 , the ratio of 10 - pound boxes : 20 - pound boxes should be 1 : 1 . the number of 10 pound boxes remains the same so we still have 4 of them . to get a ratio of 1 : 1 , the number of 20 - pound boxes must be 4 . we need to remove 12 of the 20 - pound boxes . the answer is b ."
Answer: b
Python program:
a = 20 * 20
b = 20 * 18
c = a - b
d = 20 - 10
e = c / d
f = 10 * e
g = 20 * 20
h = 20 * 18
i = g - h
j = 20 - 10
k = i / j
l = 20 - k
m = 20 * l
n = f + m 
o = 20 * 15
p = n - o
q = 20 - 15
r = p / q
Problem: the monthly rent of a shop of dimension 18 feet × 20 feet is rs . 3600 . what is the annual rent per square foot of the shop ?
Options: a ) 120 , b ) 56 , c ) 68 , d ) 87 , e ) 92
Rationale: "sol . monthly rent per square feet = 3600 / ( 18 * 20 ) = 10 & annual rent per square feet = 12 * 10 = 120 answer : a"
Answer: a
Python program:
a = 10 + 2 
b = 3600 / rectangle_area
c = a * b
Problem: a van takes 6 hours to cover a distance of 378 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 70 kmph , d ) 42 kmph , e ) 90 kmph
Rationale: "time = 6 distence = 378 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 378 / 9 = 42 kmph d"
Answer: d
Python program:
a = 3 / 2
b = a * 6
c = 378 / b
Problem: country x taxes each of its citizens an amount equal to 14 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 52,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.14 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 5,600 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,400 - - > x = 52,000 . answer : b ."
Answer: b
Python program:
a = 4 * 10
b = a * 1000
c = 4 * 2
d = c * 1000
e = 14 / 100
f = 4 * 10
g = f * 1000
h = e * g
i = d - h
j = 20 / 100
k = i / j
l = b + k
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 18.75 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 23 % , c ) 25 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 118.75 let marked price be rs . x . then , 95 / 100 x = 118.75 x = 11875 / 95 = rs . 125 now , s . p . = rs . 125 , c . p . = rs . 100 profit % = 25 % . answer : c"
Answer: c
Python program:
a = 100 + 18 
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
Problem: a sum of 15,600 amounts to 21,200 in 5 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 2 % , b ) 1 % , c ) 7 % , d ) 5 % , e ) 8 %
Rationale: "c 7 % s . i . = ( 21200 - 15600 ) = 5600 . rate = ( 100 x 5600 ) / ( 15600 x 5 ) % = 7 %"
Answer: c
Python program:
a = 3 / 4
b = 3 * 4
c = const_0_25 + const_0_25 
d = b + c 
e = a / d
f = e * 100
Problem: a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 8 gallons of water and 16 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 120 , b ) 75 , c ) 100 , d ) 150 , e ) 175
Rationale: "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 16 gallons salt is added and 8 gallons of water is added . so salt now becomes - > ( 0.2 x + 16 ) and water - - > ( 0.6 x + 8 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 16 ) = ( 0.6 x + 8 ) / 2 = > 0.2 x = 24 solving , x = 120 answer : a"
Answer: a
Python program:
a = 16 * 2
b = a - 8
c = 20 / 100
d = 1 - c
e = 20 / 100
f = 1 - e
g = 1 / 4
h = f * g
i = d - h
j = 20 / 100
k = 2 * j
l = i - k
m = b / l
Problem: rs . 6000 is lent out in two parts . one part is lent at 7 % p . a simple interest and the other is lent at 8 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 5 : 1 , b ) 5 : 5 , c ) 5 : 8 , d ) 5 : 4 , e ) 5 : 2
Rationale: "let the amount lent at 7 % be rs . x amount lent at 8 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 8 / 100 ( 6000 - x ) = 480 - x / 100 = > 480 - 1 / 100 x = 450 = > x = 3000 amount lent at 10 % = 3000 required ratio = 3000 : 3000 = 5 : 5 answer : b"
Answer: b
Python program:
a = 450 * 100
b = 6000 * 7
c = a - b
d = 8 - 7
e = c / d
f = 450 * 100
g = 6000 * 7
h = f - g
i = 8 - 7
j = h / i
k = e / j
Problem: we invested a total of $ 1,000 . we invested one part of the money at 4 % and the rest of the money at 6 % . the total investment with interest at the end of the year was $ 1,046 . how much money did we invest at 4 % ?
Options: a ) $ 600 , b ) $ 650 , c ) $ 700 , d ) $ 750 , e ) $ 800
Rationale: let x be the money invested at 4 % . 1.04 x + 1.06 ( 1000 - x ) = 1046 . 0.02 x = 1060 - 1046 . 0.02 x = 14 . 2 x = 1400 . x = 700 . the answer is c .
Answer: c
Python program:
a = 2 + 3 
b = a * 2
c = 100 * b
d = 6 / 100
e = d + 1 
f = c * e
g = 2 + 3 
h = g * 2
i = 100 * h
j = 2 + 3 
k = j * 2
l = k * 4
m = i + l 
n = 2 * 3
o = m + n 
p = f - o
q = 6 / 100
r = q + 1 
s = 4 / 100
t = s + 1 
u = r - t
v = p / u