euclaise/mathqa_programs huggingface dataset:
Problem: mary and mike enter into a partnership by investing $ 800 and $ 200 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1200 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 3000 , b ) $ 3500 , c ) $ 4000 , d ) $ 4200 , e ) $ 4500
Rationale: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 8 : 2 . i . e . , 80 % of 2 x would go to mary and 20 % of 2 x would go to mike . hence , mary would get ( 80 - 20 ) % of 2 x more than mike or 60 % of 2 x = $ 1200 i . e . , ( 60 / 100 ) * 2 x = 1200 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : a"
Answer: a
Python program:
a = 800 / 1000
b = 200 / 1000
c = a - b
d = 1 / 3
e = 1 - d
f = c * e
g = 1200 / f
Problem: the ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 4332 sq cm . what is the ratio of the width and the area of the rectangle ?
Options: a ) 1 : 72 , b ) 1 : 76 , c ) 1 : 80 , d ) 1 : 84 , e ) 1 : 88
Rationale: "let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 4332 12 x ^ 2 = 4332 x ^ 2 = 361 x = 19 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 76 the answer is b ."
Answer: b
Python program:
a = 3 * 4332
b = math.sqrt(a)
c = b / 2
d = c / 4332
Problem: if a and b are positive numbers , and a ^ 3 + b ^ 3 = 30 , then the greatest possible value of a is between :
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
Rationale: "if a = 3.1 and b is very small , then a ^ 3 + b ^ 3 can equal 30 . if a > 4 , then a ^ 3 + b ^ 3 > 30 . the answer is b ."
Answer: b
Python program:
a = 1/(3)
b = 30 ** a
c = math.floor(b)
d = c * 10
e = 1/(3)
f = 30 ** e
g = math.floor(f)
h = g + 1 
i = d + h
Problem: an owner of a pizza stand sold small slices of pizza for rs . 150 each and large slices for rs . 250 each . one night he sold 5000 slices , for a total of rs . 10.50 lakh . how many small slices were sold ?
Options: a ) 3000 , b ) 2000 , c ) 4000 , d ) 2500 , e ) 3500
Rationale: explanatory answer this question is a word problem in linear equations . the problem is solved by framing two linear equations from the information given in the question and solving them . let ' s ' be the number of small slices and ' b ' the number of large slices sold on that night . therefore , s + b = 5000 . . . eqn ( 1 ) each small slice was sold for rs . 150 . therefore , ' s ' small slices would have fetched rs . 150 s . each large slice was sold for rs . 250 . therefore , ' b ' large slices would have fetched rs . 250 b . total value of sale = 150 s + 250 b = 10 , 50000 ( note the left hand side is in rupees and hence we have to convert right hand also to rupees from lakhs of rupees ) or 150 s + 250 b = 10 , 50000 . . . eqn ( 2 ) multiplying equation ( 1 ) by 150 , we get 150 s + 150 b = 7 , 50000 . . . eqn ( 3 ) subtracting eqn ( 3 ) from eqn ( 2 ) , we get 100 b = 300000 or b = 3000 we know that s + b = 5000 so , s = 5000 - b = 5000 - 3000 = 2000 . 2000 small slices were sold . answer b
Answer: b
Python program:
a = 3 * 1000
b = 5000 - a
Problem: a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 189 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 189 km time taken = distance / speed = 189 / 27 = 7 hours . answer : option e"
Answer: e
Python program:
a = 22 + 5 
b = 189 / a
Problem: light glows for every 21 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 236 times , c ) 382 times , d ) 392 times , e ) 482 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 21 ) = 236 times . answer : b"
Answer: b
Python program:
a = 2 + 47 
b = 2 + const_60 
c = 20 + b 
d = c * const_60
e = a + d 
f = e / 21
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 240 m long ?
Options: a ) 40 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 240 = 600 m required time = 600 * 2 / 25 = 48 sec answer : d"
Answer: d
Python program:
a = 45 - 240
b = a * const_0_2778
c = 360 / b
Problem: a man buys a cycle for rs . 1400 and sells it at a loss of 12 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1160 , c ) s . 1232 , d ) s . 1202 , e ) s . 1204
Rationale: "since , c . p = 1400 loss % = ( c . p - s . p ) / c . p * 100 12 = ( 1400 - s . p ) / 1400 * 100 so , after solving answer = 1232 . answer : c"
Answer: c
Python program:
a = 100 - 12
b = a * 1400
c = b / 100
Problem: all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes have only one face coloured ?
Options: a ) 4 , b ) 8 , c ) 16 , d ) 24 , e ) 2
Rationale: "there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having only one face coloured = ( x - 2 ) 2 x no . of faces = ( 4 - 2 ) ^ 2 x 6 = 24 answer : d"
Answer: d
Python program:
a = 64 / 4
b = a / 2
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 20 percent on clothing , 50 percent on food , and 30 percent on other items . if jill paid a 10 percent tax on the clothing , 15 percent tax on the food , and no tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 12.45 , b ) 12.5 , c ) 12.65 , d ) 12.35 , e ) 12.25
Rationale: "assume she has $ 200 to spend . tax clothing = 20 % = $ 40 = $ 10.00 food = 50 % = $ 100 = $ 15.00 items = 30 % = $ 60 = $ 0.00 total tax = $ 25.00 % of total amount = 25 / 200 * 100 = 12.25 % answer e"
Answer: e
Python program:
a = 10 / 100
b = 20 * a
c = 15 / 100
d = 30 * c
e = b + d 
f = e / 100
g = f * 100
Problem: if there are 26 laborers in a crew , and on a certain day , 10 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
Options: a ) 39.5 % , b ) 38.5 % , c ) 36.5 % , d ) 37.5 % , e ) 30.5 %
Rationale: "10 / 26 * 100 = 38.46 38.5 % correct answer b"
Answer: b
Python program:
a = 10 * 100
b = a / 26
Problem: how many 3 - digit numbers can be formed from the digits 2 , 3 , 5 , 6 , 7 and 9 , which are divisible by 5 and if the repetition is allowed ?
Options: a ) 20 , b ) 5 , c ) 10 , d ) 36 , e ) 25
Rationale: "since , each desired number is divisible by 5 , so we must have 5 at the unit place . so , the tens place can now be filled by any of the remaining 6 digits ( 2 , 3 , 6 , 7 , 9 , 5 ) therefore the 3 - digit no can be formed by ( 6 * 6 * 1 ) = 36 ways - - - - - - ( since repetition is allowed ) ans - d"
Answer: d
Python program:
a = 5 * 4
Problem: the profit obtained by selling an article for rs . 66 is the same as the loss obtained by selling it for rs . 52 . what is the cost price of the article ?
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 49 , d ) rs . 59 , e ) none of these
Rationale: "s . p 1 - c . p = c . p – s . p 2 66 - c . p = c . p - 52 2 c . p = 66 + 52 ; c . p = 118 / 2 = 59 answer : d"
Answer: d
Python program:
a = 66 + 52 
b = a / 2
Problem: if 7 and 9 are factors of 60 n , what is the minimum value of n ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 14 , e ) 21
Rationale: "60 n / 7 * 9 should be integer = > 2 * 2 * 3 * 5 * n / 7 * 3 * 3 = 2 * 2 * 5 * n / 21 must be an integer for this to be true n must multiple of 21 , thus min of n = 21 hence e"
Answer: e
Python program:
a = math.lcm(7, 9)
Problem: a bag contains 5 red , 4 blue and 3 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 33 , d ) 4 / 27 , e ) 3 / 23
Rationale: "p ( both are red ) , = 5 c 212 c 2 = 5 c 212 c 2 = 10 / 66 = 5 / 33 c"
Answer: c
Python program:
a = math.comb(5, 2)
b = 5 + 4 
c = b + 3 
d = math.comb(c, 2)
e = a / d
Problem: in an election between two candidates , the first candidate got 70 % of the votes and the second candidate got 240 votes . what was the total number of votes ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200
Rationale: "let v be the total number of votes . 0.3 v = 240 v = 800 the answer is a ."
Answer: a
Python program:
a = 240 * 100
b = 100 - 70
c = a / b
Problem: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 38 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 86.66 % , e ) 66.66 %
Rationale: - - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 38 % 0.4 x + ( m - x ) 0.25 = 0.38 m 0.15 x = 0.13 m x = 0.8666 m x = 86.66 % of m d
Answer: d
Python program:
a = 38 - 25
b = 40 / 100
c = 25 / 100
d = b - c
e = a / d
Problem: find the product of the localvalue and absolutevalue of 5 in 20568 ?
Options: a ) 1000 , b ) 2500 , c ) 1200 , d ) 5000 , e ) 1600
Rationale: "local value of 5 = 5 x 100 = 500 place value of 5 = 5 there fore = 5 x 500 = 2500 b"
Answer: b
Python program:
a = 5 * 1000
b = a * 5
Problem: a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 9.09 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 20 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 10 / 11 = ( 1 + p % ) profit % = 25 % answer : d"
Answer: d
Python program:
a = 100 + 10 
b = 100 - 20
c = 9 + 9 
d = a - c
e = d * 2
Problem: a sum of rs . 2665 is lent into two parts so that the interest on the first part for 5 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) rs . 1178.55 , b ) rs . 1978.25 , c ) rs . 1332.5 , d ) rs . 1678 , e ) rs . 1675.55
Rationale: "( x * 5 * 3 ) / 100 = ( ( 2665 - x ) * 3 * 5 ) / 100 15 x / 100 = 39975 / 100 - 15 x / 100 30 x = 39975 = > x = 1332.5 second sum = 2665 – 1025 = 1332.5 answer : c"
Answer: c
Python program:
a = 3 * 5
b = a * 2665
c = 3 * 5
d = 5 * 3
e = c + d 
f = b / e
g = 2665 - f
Problem: 2 , 3 , 6 , 15 , _ , 123 ?
Options: a ) 42 , b ) 38 , c ) 28 , d ) 29 , e ) 11
Rationale: answer : a
Answer: a
Python program:
a = negate - (
Problem: nitin ranks 15 th in a class of 47 students . what is rank from the last ?
Options: a ) 33 , b ) 38 , c ) 32 , d ) 28 , e ) 19
Rationale: "explanation : number students behind the nitin in rank = ( 47 - 15 ) = 32 nitin is 33 rd from the last answer : a ) 33"
Answer: a
Python program:
a = 47 - 15
Problem: cole drove from home to work at an average speed of 70 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78
Rationale: "let the distance one way be x time from home to work = x / 70 time from work to home = x / 105 total time = 2 hrs ( x / 70 ) + ( x / 105 ) = 2 solving for x , we get x = 84 time from home to work in minutes = ( 84 ) * 60 / 70 = 72 minutes ans = c"
Answer: c
Python program:
a = 105 * 2
b = 70 + 105 
c = a / b
d = c * const_60
Problem: what is the least common multiple of 152 and 190 ?
Options: a ) 304 , b ) 14440 , c ) 760 , d ) 28880 , e ) 1520
Rationale: "yes there is a shorter way 152 = 2 * 2 * 2 * 19 190 = 2 * 5 * 19 i think everyone knows how to do this . then choose 2 * 2 * 2 and choose 5 and choose 19 2 * 2 * 2 * 5 * 19 = 760 answer is c"
Answer: c
Python program:
a = 152 + 1 
b = a * 2
Problem: in how many ways can an answer key for a quiz be written if the quiz contains 5 true - false questions followed by 3 multiple - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 1220 , b ) 1650 , c ) 1920 , d ) 2440 , e ) 2860
Rationale: "there are 2 ^ 5 = 32 possibilities for the true - false answers . however we need to remove two cases for ttttt and fffff . there are 4 * 4 * 4 = 64 possibilities for the multiple choice questions . the total number of possibilities is 30 * 64 = 1920 . the answer is c ."
Answer: c
Python program:
a = 3 ** 5
b = a - 3
c = 4 * 4
d = b * c
Problem: canister c is 1 / 2 full of water and canister d , which has twice the capacity of canister c , is 1 / 3 full of water . if the water in canister d is poured in canister c until canister c is completely full of water , canister d will still contain what fraction of its capacity of water ?
Options: a ) 0 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 4
Rationale: say canister c has a capacity of 6 liters . it ' s half full , thus there can be poured 3 liters of water . canister b is 12 liters and there are 4 liters of water . we can pour 3 liters from d to c and 1 liter will still be left in d , which is 1 / 12 of its total capacity . answer : c .
Answer: c
Python program:
a = 1 / 3
b = 1 / 2
c = 1 / 2
d = b * c
e = a - d
Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 6000 . their h . c . f is ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 100
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 6000 x = 100 the numbers are 3 * 100 , 4 * 100 , 5 * 100 hence required h . c . f . = 100 answer is e"
Answer: e
Python program:
a = 3 * 5
b = a * 100
c = 4 * 5
d = b + c
Problem: jose is uploading a file to the internet for a college project . the file weighs 160 megabytes . if jose ' s internet speed for uploading tops 8 megabytes per minute , how long will it take until the upload is completed ?
Options: a ) 1 hour , b ) 45 minutes , c ) 20 minutes , d ) 5 minutes , e ) 1 hour and 10 minutes
Rationale: answer is ( c ) . jose calculates that if the files weighs 160 megabytes , and his internet uploads at 8 megabytes per minute , it would take 20 minutes to upload as 160 divided by 8 megabytes per minute equals 20 .
Answer: c
Python program:
a = 160 / 8
Problem: the average monthly salary of 20 employees in an organisation is rs . 1600 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) 3700 , b ) 3890 , c ) 88798 , d ) 2789 , e ) 2891
Rationale: "explanation : manager ' s monthly salary rs . ( 1700 * 21 - 1600 * 20 ) = rs . 3700 . answer : a ) 3700"
Answer: a
Python program:
a = 1600 + 100 
b = 20 + 1 
c = a * b
d = 1600 * 20
e = c - d
Problem: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 19000 left with him . find salary . .
Options: a ) $ 10900 , b ) $ 19000 , c ) $ 190000 , d ) $ 1900 , e ) none
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 19000 , = [ 1 - 9 / 10 ] * total salary = $ 19000 , total salary = $ 19000 * 10 = $ 190000 , correct answer ( c )"
Answer: c
Python program:
a = 1 / 5
b = 1 / 10
c = a + b 
d = 3 / 5
e = c + d 
f = 1 - e
g = 19000 / f
Problem: in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 30 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 69.10 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 30 % of 1100 ) + ( 32 % of 900 ) = 330 + 288 = 618 failed = 2000 - 618 = 1382 failed % = [ ( 1382 / 2000 ) x 100 ] % = 69.1 % . answer : d"
Answer: d
Python program:
a = 100 * 10
b = 2 * a
c = 30 / 100
d = 100 * 10
e = 2 * d
f = e - 900
g = c * f
h = b - g
i = 32 / 100
j = i * 900
k = h - j
l = 100 * 10
m = 2 * l
n = k / m
o = n * 100
Problem: if 2 x + y = 7 and x + 2 y = 10 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 9 , d ) 18 / 5 , e ) 4
Rationale: "we have two equations : 2 x + y = 7 x + 2 y = 10 notice that something nice happens when we add them . we get : 3 x + 3 y = 17 divide both sides by 3 to get : x + y = 17 / 3 so , ( x + y ) / 3 = 17 / 9 answer : c"
Answer: c
Python program:
a = 7 * 2
b = a - 10
c = 2 * 2
d = c - 1
e = b / d
f = 7 * 2
g = f - 10
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 7 - k
m = e + l 
n = m / 3
Problem: two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 40 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 110 , c ) 120 , d ) 16 , e ) 180
Rationale: "c 120 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 40 mph = 120 miles"
Answer: c
Python program:
a = 36 / 2
b = a / 6
c = 40 * b
Problem: puzzle ! ! ! 🙂 if 111 = 09 444 = 12 777 = 15 then 888 = ? ? ?
Options: a ) 13 , b ) 17 , c ) 18 , d ) 11 , e ) 15
Rationale: e 15 one + one + one ( 3 + 3 + 3 ) = 09 four + four + four ( 4 + 4 + 4 ) = 12 seven + seven + seven ( 5 + 5 + 5 ) = 15 therefore eight + eight + eight ( 5 + 5 + 5 ) = 15
Answer: e
Python program:
a = 15 * 1
Problem: town m town n town o town p town q town r ; town a town b town c town d town e town f in the table above , what is the least number of table entries that are needed to show the mileage between each town and each of the other 5 towns ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: easy way to go about this problem is we have 6 * 6 = 36 enteries in table the least number of enteries would be ( 36 - 6 ) / 2 since 6 enteries represent the distances between same points . alternatively this can be solved as combination problem . correct answer e
Answer: e
Python program:
a = 2 * 3
b = a * 5
c = b / 2
Problem: what is the greatest of 3 consecutive integers whose sum is 33 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "33 / 3 = 11 the three numbers are 10 , 11 , and 12 . the answer is c ."
Answer: c
Python program:
a = 33 - 3
b = a / 3
c = b + 2
Problem: a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 45 - sided polygon have ?
Options: a ) 875 , b ) 945 , c ) 1425 , d ) 2025 , e ) 2500
Rationale: "there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 45 . plugging it in , we get 945 diagonals ! answer ( b ) ."
Answer: b
Python program:
a = 45 - 3
b = a * 45
c = b / 2
Problem: divide rs . 1600 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) rs . 800 , b ) rs . 400 , c ) rs . 600 , d ) rs . 500 , e ) rs . 900
Rationale: "a + b + c = 1600 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1600 = > 400 answer : b"
Answer: b
Python program:
a = 1600 / 3
Problem: 112 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 26 , c ) 49 , d ) 27 , e ) 11
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 112 = 49 answer : c"
Answer: c
Python program:
a = 4 + 3 
b = 4 + 3 
c = b + 2 
d = a / c
e = d * 112
f = e / 2
Problem: a , b and c started a shop by investing rs . 5,000 , rs . 15,000 and rs . 30,000 respectively . at the end of the year , the profits were distributed among them . if c â € ™ s share of profit be rs . 3000 , then the total profit was :
Options: a ) 30,000 , b ) 5,000 , c ) 80,000 , d ) 120,000 , e ) none
Rationale: sol . a : b : c = 5000 : 15000 : 30000 = 1 : 3 : 6 . so , c â € ™ s share : total profit = 6 : 10 let the total profit be rs . x . then , 6 / 10 = 3000 / x or x = 3000 * 10 / 6 = 5000 . answer b
Answer: b
Python program:
a = 2 + 3 
b = 2 + 3 
c = b * 2
d = a * c
e = d * 100
f = 2 + 3 
g = 2 + 3 
h = g * 2
i = f * h
j = i * 100
k = j * 3
l = e + k 
m = 2 + 3 
n = 2 + 3 
o = n * 2
p = m * o
q = p * 100
r = q * 3
s = r * 2
t = l + s 
u = 2 + 3 
v = 2 + 3 
w = v * 2
x = u * w
y = x * 100
z = y * 3
A = z * 2
B = 3000 / A
C = t * B
Problem: christine selects an item at a 25 % off ticket price sale . the item is ticket priced at $ 25 . how much should christine expect to pay at the register ?
Options: a ) 22.5 , b ) 20.0 , c ) 18.75 , d ) 12.5 , e ) 10.0
Rationale: r . p . = $ 25.00 sale % = 25 s . p . = r . p . * ( 1 - ( sale % / 100 ) ) = 25 * ( 1 - ( 25 / 100 ) ) = 18.75 answer : c
Answer: c
Python program:
a = 25 * 25
b = a / 100
c = 25 - b
Problem: two employees x and y are paid a total of rs . 500 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 227 , b ) s . 287 , c ) s . 297 , d ) s . 300 , e ) s . 380
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 500 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 500 ⇒ y [ 12 / 10 + 1 ] = 500 ⇒ 22 y / 10 = 500 ⇒ 22 y = 5000 ⇒ y = 5000 / 22 = rs . 227.77 a )"
Answer: a
Python program:
a = 1 + 4 
b = a * 2
c = 500 * b
d = 1 + 4 
e = d * 2
f = e + 1 
g = f * 2
h = c / g
Problem: if the perimeter of square region e and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2 : 3 then the ratio of the area of r to the area of e
Options: a ) 25 : 16
b ) 24 : 25
c ) 5 : 6
d ) 4 : 5
e ) 4 : 9
Rationale: we know perimeter of a square ( pe ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pe = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b
Answer: b
Python program:
a = rectangle_area / (
Problem: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 30 days to complete the same work . then q alone can do it in
Options: a ) 10 , b ) 22 , c ) 25 , d ) 27 , e ) 30
Rationale: work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 30 work done by p , q and r in 1 day = 1 / 10 + 1 / 30 = 4 / 30 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 4 / 30 = > work done by p in 1 day = 4 / 60 = > work done by q and r in 1 day = 4 / 60 hence work done by q in 1 day = 4 / 60 â € “ 1 / 30 = 2 / 60 = 1 / 30 so q alone can do the work in 30 days answer is e .
Answer: e
Python program:
a = 1 / 10
b = 1 / 30
c = a + b 
d = c / 2
e = 1 / 30
f = d - e
g = 1 / f