euclaise/mathqa_programs huggingface dataset:
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 5 % p . a . was rs . 246 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 2535 , b ) rs . 2646 , c ) rs . 2546 , d ) rs . 2656 , e ) rs . 2565
Rationale: "let the sum be rs . p p { [ 1 + 5 / 100 ] 2 - 1 } = 246 p ( 5 / 100 ) ( 2 + 5 / 100 ) = 246 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 246 / ( 0.05 ) ( 2.05 ) = 2400 . amount = rs . 2646 answer : b"
Answer: b
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = 246 / d
f = e + 246
Problem: the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1800 , then what is the income of p 1 ?
Options: a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 3200 , e ) s . 4500
Rationale: "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 1800 … ( i ) and 4 x – 2 y = 1800 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1800 - > x = 900 p 1 ’ s income = rs 5 * 900 = rs . 4500 answer : e"
Answer: e
Python program:
a = 1800 / 2
b = a * 3
c = b - 1800
d = c * 5
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 100 per component . shipping costs for delivering the components are $ 4 per unit . further , the manufacturer has costs of $ 24,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 100 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) 278 , b ) 366 , c ) 349 , d ) 335 , e ) 295
Rationale: "$ 24500 is a fixed cost each component is $ 104 ( $ 100 to produce , $ 4 to ship ) manufacturer will be producing and selling 100 components so therefore the equation to find price would be 100 * p = 24500 + ( 100 * 100 ) + ( 100 * 4 ) p = ( 24500 + 10000 + 400 ) / 100 p = 349 answer : c"
Answer: c
Python program:
a = 4 * 4
b = a * 1000
c = 4 * 100
d = b + c 
e = 100 + 4 
f = e * 100
g = d + f 
h = g / 100
Problem: a number when divided by 45 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 21
Options: a ) a ) 15 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7
Rationale: "explanation : p ÷ 45 = 432 = > p = 432 * 45 = 19440 p / 31 = 19440 / 21 = 925 , remainder = 15 answer : option a"
Answer: a
Python program:
a = 45 * 432
b = a / 21
Problem: the average temperature for tuesday , wednesday and thursday was 45 ° c . the average temperature for wednesday , thursday and friday was 50 ° c . if the temperature on friday be 53 ° c , what was the temperature on tuesday ?
Options: a ) 39 ° c , b ) 44 ° c , c ) 37 ° c , d ) 42 ° c , e ) 38 c
Rationale: "explanation : t + w + t = 45 × 3 = 135 ° c w + t + f = 50 × 3 = 150 ° c also , temperature on friday = 53 ° c temperature on tuesday = 135 + 53 - 150 = 38 ° c answer : option e"
Answer: e
Python program:
a = 45 * 3
b = 50 * 3
c = b - 53
d = a - c
Problem: if ( c - a ) / ( c - b ) = 1 , then ( 5 b - 2 a ) / ( c - a ) =
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 6
Rationale: let ' s say c = 3 , b = 2 , a = 2 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 6 answer e ( hopefully ) ) )
Answer: e
Python program:
a = 5 - 2
b = a * 2
Problem: the sum of three consecutive numbers is 87 . the greatest among these three numbers is :
Options: a ) 22 , b ) 24 , c ) 26 , d ) 30 , e ) 44
Rationale: "sol . let the numbers be x , x + 1 and x + 2 . then , x + ( x + 1 ) + ( x + 2 ) = 87 ⇔ 3 x = 84 ⇔ x = 28 . greatest number = ( x + 2 ) = 30 . answer d"
Answer: d
Python program:
a = 87 + 1 
b = a / 2
Problem: in a group of 22 boys , 13 play basketball and 15 play football . 3 of the boys play neither . how many play both ?
Options: a ) 18 , b ) 20 , c ) 21 , d ) 22 , e ) 25
Rationale: 18 boys play something . if b play both , then 13 + 15 - b = 18 answer is a
Answer: a
Python program:
a = 13 + 15 
b = 22 - 3
c = b - 15
d = 22 - 3
e = d - 13
f = c + e 
g = a - f
Problem: a polygon has 44 diagonals , then the number of its sides are
Options: a ) 11
b ) 9
c ) 7
d ) 5
e ) 3
Rationale: let the number of sides be n . the number of diagonals is given by nc 2 - n therefore , nc 2 - n = 44 , n > 0 n ( n - 1 ) / 2 - n = 44 n 2 - 3 n - 88 = 0 n 2 - 11 n + 8 n - 88 = 0 n ( n - 11 ) + 8 ( n - 11 ) = 0 n = - 8 or n = 11 . answer : a
Answer: a
Python program:
a = 3 ** 2
b = 44 * 2
c = b * 4
d = a + c 
e = math.sqrt(d)
f = e + 3 
g = f / 2
Problem: the cash difference between the selling prices of an article at a profit of 2 % and 6 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 53 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 55 , e ) none of these
Rationale: "explanation : let the cost price of article is rs . x required ratio = ( 102 % of x ) / ( 106 % of x ) = 102 / 106 = 51 / 53 = 51 : 53 . answer : a"
Answer: a
Python program:
a = 100 + 2 
b = 100 + 6 
c = a / b
Problem: two trains of equal length , running with the speeds of 60 and 60 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 1.0 , b ) 8.2 , c ) 7.7 , d ) 2.6 , e ) 8.3
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 60 = 120 * 5 / 18 t = 2500 / 9 * 18 / 600 = 8.3 sec . answer : e"
Answer: e
Python program:
a = 60 - 60
b = const_0_2778 * a
c = b * 50
d = 60 + 60 
e = const_0_2778 * d
f = 1/(e)
g = c * f
Problem: in a certain village , 200 litres of water are required per household per month . at this rate , if there are 10 households in the village , how long ( in months ) will 2000 litres of water last ?
Options: a ) 1 , b ) 20 , c ) 2 , d ) 200 , e ) 2.5
Rationale: "i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 200 litres of water are required per household per month . at this rate , if there aren 10 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 200 * 10 = 2000 ( m * n ) water available is 2000 ( p ) it will last 1 months ( p / m * n ) answer ( a )"
Answer: a
Python program:
a = 200 * 10
b = 2000 / a
Problem: in a factory , there are 80 % technicians and 20 % non - technicians . if the 80 % of the technicians and 20 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 62 % , b ) 68 % , c ) 52 % , d ) 22 % , e ) 42 %
Rationale: "total = 100 t = 80 nt = 20 80 * ( 20 / 100 ) = 24 80 * ( 20 / 100 ) = 24 16 + 16 = 32 = > 100 - 32 = 68 % answer : b"
Answer: b
Python program:
a = 20 / 100
b = 80 * a
c = 80 / 100
d = c * 20
e = b + d 
f = 100 - e
Problem: what is the units digit of ( 147 ^ 21 ) ^ 48 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 21 has the form 4 n + 1 so the units digit is 7 inside the bracket . the number 48 has the form 4 n , so the units digit is 1 . the answer is a .
Answer: a
Python program:
a = 4 + 3 
b = a + 2
Problem: what percentage of numbers from 1 to 70 have 1 or 9 in the unit ' s digit ?
Options: a ) 10 % , b ) 30 % , c ) 20 % , d ) 70 % , e ) 45 %
Rationale: d 20 % clearly , the numbers which have 1 or 9 in the unit ' s digit , have squares that end in the digit 1 . such numbers from 1 to 70 are 1 , 9 , 11 , 19 , 21 , 29 , 31 , 39 , 41 , 49 , 51 , 59 , 61 , 69 . number of such number = 14 required percentage = ( 14 x 100 / 70 ) % = 20 % .
Answer: c
Python program:
a = 70 / 10
b = 2 * a
c = b / 70
d = c * 100
Problem: what is the measure of the radius of the circle inscribed in a triangle whose sides measure 8 , 15 and 19 units ?
Options: a ) 2.8 units , b ) 6 units , c ) 3 units , d ) 5 units , e ) 12 units
Rationale: "sides are 8 , 15 and 19 . . . thus it is right angle triangle since 19 ^ 2 = 8 ^ 2 + 15 ^ 2 therefore , area = 1 / 2 * 15 * 8 = 60 we have to find in - radius therefore , area of triangle = s * r . . . . where s = semi - perimeter and r = in - radius now s = semi - perimeter = 19 + 15 + 8 / 2 = 21 thus , 60 = 21 * r and hence r = in - radius = 2.8 option a"
Answer: a
Python program:
a = triangle_area_three_edges / (
Problem: 12 is what % of 80 ?
Options: a ) 6 , b ) 6.67 , c ) 12 , d ) 13 , e ) 15
Rationale: "we assume that 80 is 100 % assume ' x ' is value we looking for here , 80 = 100 % and x % = 12 therefore , 100 / x = 80 / 12 100 / x = 6.6667 x = 15 e"
Answer: e
Python program:
a = 12 / 80
b = a * 100
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 1.20 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 255 , b ) $ 275 , c ) $ 510 , d ) $ 612 , e ) $ 2,550
Rationale: total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 1.20 = $ 612 answer d
Answer: d
Python program:
a = 1000 * 1000
b = 3 * 6
c = 20 * 20
d = c * 15
e = b / d
f = e * 1
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 40 % , then the cost price of the article is :
Options: a ) 500 , b ) 277 , c ) 222 , d ) 297 , e ) 400
Rationale: "explanation : 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 100 * 560 ) / 140 = rs . 400 answer : e"
Answer: e
Python program:
a = 616 * 100
b = 100 + 10 
c = a / b
d = 100 + 10 
e = c * d
f = 100 + 40 
g = e / f
Problem: find l . c . m of 852 and 1491
Options: a ) 5964 , b ) 5664 , c ) 4964 , d ) 4664 , e ) 5555
Rationale: 852 ) 1491 ( 1 852 639 ) 852 ( 1 639 213 ) 639 ( 3 639 0 h . c . f of 852 and 1491 is 213 : . l . c . m = 852 * 1491 / 213 = 5964 answer is a .
Answer: a
Python program:
a = 2 ** 2
b = 3 * a
c = 852 / 2
d = c / 2
e = d / 3
f = b * e
g = 4 + 3 
h = f * g
Problem: how many positive integers less than 300 are there such that they are multiples of 17 or multiples of 16 ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "300 / 17 = 17 ( plus remainder ) so there are 17 multiples of 17 300 / 16 = 18 ( plus remainder ) so there are 18 multiples of 16 we need to subtract 1 because 17 * 16 is a multiple of both so it was counted twice . the total is 17 + 18 - 1 = 34 the answer is d ."
Answer: d
Python program:
a = 4 + 17 
b = a - 1
c = math.factorial(b)
d = math.factorial(17)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 25 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 5 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) none of these
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 25 : â ˆ š 9 = 5 : 3 . answer b"
Answer: b
Python program:
a = math.sqrt(25)
b = math.sqrt(9)
c = a / b
Problem: convert 700 miles into meters ?
Options: a ) 784596 , b ) 1126538 , c ) 804670 , d ) 784596 , e ) 864520
Rationale: "1 mile = 1609.34 meters 700 mile = 700 * 1609.34 = 1126538 meters answer is b"
Answer: b
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 700
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: when the positive integer a is divided by 11 , the quotient is b and the remainder 3 . when a is divided by 19 , the remainder is also 3 . what is the remainder when b is divided by 19 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: any number which when divided by divisor d 1 , d 2 , etc . leaving same remainderrtakes the form ofk + r where k = lcm ( d 1 , d 2 ) in this case the divisors are 1119 and remainder is 3 . so lcm ( 11,19 ) = 209 so n = 209 + 3 = 212 also a = d 1 q + 3 ; which means d 1 q = 209 d 1 = 11 therefore q = 19 and ( b divided by 19 ) 19 / 19 leaves remainder 0 . answer is e
Answer: e
Python program:
a = reminder + (
Problem: yearly subscription to professional magazines cost a company $ 940.00 . to make a 35 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 655 , c ) 611 , d ) 657 , e ) 658
Rationale: "total cost 940 940 * 35 / 100 = 329 so the cut in amount is 329 the less amount to be spend is 940 - 329 = 611 answer : c"
Answer: c
Python program:
a = 100 - 35
b = a / 100
c = b * 940
Problem: a certain article of clothing was discounted during a special sale to 2 / 3 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 22.22 % , c ) 25 % , d ) 16.66 % , e ) 12.5 %
Rationale: "say the original retail price of the item was $ 200 . the price after the first sale = 2 / 3 * $ 200 = $ 400 / 3 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 400 / 3 - 100 ) / 150 = 1 / 3 = 22.22 % . answer : b ."
Answer: b
Python program:
a = 2 / 3
b = 2 / 3
c = 1 / 2
d = b * c
e = a - d
f = e * 100
Problem: rates for having a manuscript typed at a certain typing service are $ 10 per page for the first time a page is typed and $ 5 per page each time a page is revised . if a certain manuscript has 100 pages , of which 20 were revised only once , 30 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 1200 , b ) $ 1500 , c ) $ 1400 , d ) $ 1250 , e ) $ 1350
Rationale: "50 pages typed 1 x 20 pages typed 2 x ( original + one revision ) 30 pages typed 3 x ( original + two revisions ) 50 ( 10 ) + 20 ( 10 + 5 ) + 30 ( 10 + 5 + 5 ) = 500 + 300 + 600 = 1400 answer - c"
Answer: c
Python program:
a = 100 * 10
b = 20 * 5
c = a + b 
d = 30 * 5
e = d * 2
f = c + e
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 7 more than the average of 10 , 70 , and what number ?
Options: a ) 19 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 7 = 33 sum of second list = 33 * 3 = 99 therefore the number = 99 - 80 = 19 answer : a"
Answer: a
Python program:
a = 20 + 40 
b = a + 60 
c = 7 * 3
d = c + 10 
e = d + 70 
f = b - e
Problem: there are 2 sections a and b in a class , consisting of 50 and 40 students respectively . if the average weight of section a is 50 kg and that of section b is 70 kg , find the average of the whole class ?
Options: a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 58.88 kg , e ) 70.89 kg
Rationale: "total weight of 50 + 40 students = 50 * 50 + 40 * 70 = 2500 + 2800 average weight of the class is = 5300 / 90 = 58.88 kg answer is d"
Answer: d
Python program:
a = 50 * 50
b = 40 * 70
c = a + b 
d = 50 + 40 
e = c / d
Problem: dan ' s age after 20 years will be 7 times his age 4 years ago . what is the present age of dan ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "let dan ' s present age be x . x + 20 = 7 ( x - 4 ) 6 x = 48 x = 8 the answer is b ."
Answer: b
Python program:
a = 4 * 7
b = 20 + a 
c = 7 - 1
d = b / c
Problem: a work as fast as b . if b can complete a work in 12 days independently , the number of days in which a and b can together finish the work in ?
Options: a ) 2 days , b ) 3 days , c ) 4 days , d ) 5 days , e ) 6 days
Rationale: ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 6 b ' s 1 day work = 1 / 12 a + b 1 day work = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 a and b can finish the work in 4 days answer is c
Answer: c
Python program:
a = 1/(12)
b = 1/(12)
c = 2 * b
d = a + c 
e = 1/(d)
Problem: in a group of 6 boys & 4 girls a committee of 4 persons is to be formed . in how many different ways can it be done so that the committee has at least 1 girl ?
Options: a ) 187 , b ) 190 , c ) 192 , d ) 195 , e ) 213
Rationale: the committee of 4 persons is to be so formed that it has at least 1 woman the different ways that we can choose to form such a committee are : ( i ) lw . 3 m in t 6 x 5 x 4 ' x 6 c 3 = 4 x — — 80 3 x 2 x 1 x 6 c 2 = 42 : : x 26 : : = 90 ( ii ) 2 w . 2 m in ° c 2 ( iii ) 3 w . 1 m in 4 c 3 x 6 c 1 = 4 x 6 = 24 ( iv ) 4 w in 6 c 4 = 1 total no . of different ways in which a committee of 4 persons can be formed so that it has at least one woman . = 80 + 90 + 24 + 1 = 195 d
Answer: d
Python program:
a = 6 + 4 
b = math.factorial(a)
c = math.factorial(4)
d = math.factorial(6)
e = c * d
f = b / e
g = math.factorial(6)
h = math.factorial(2)
i = math.factorial(4)
j = h * i
k = g / j
l = f - k
Problem: three circles of radius 3.5 cm are placed in such a way that each circle touches the other two . the area of the portion enclosed by the circles is
Options: a ) 1.967
b ) 1.963
c ) 2.388
d ) 3.388
e ) 2.382
Rationale: explanation : required area = ( area of an equilateral triangle of side 7 cm ) - ( 3 * area of sector with ã = 60 degrees and r = 3.5 cm ) \ inline { \ color { black } ( \ frac { \ sqrt { 3 } } { 4 } \ times 7 \ times 7 ) - ( 3 \ times \ frac { 22 } { 7 } \ times 3.5 \ times 3.5 \ times \ frac { 60 } { 360 } ) } sq cm = \ inline { \ color { black } ( \ frac { \ sqrt { 3 } } { 4 } \ times 49 ) - ( 11 \ times 0.5 \ times 3.5 ) } sq cm = 1.967 sq cm answer : a ) 1.967
Answer: a
Python program:
a = 3 * 5
b = 3 * 5
c = 3 * 5
d = triangle_area_three_edges - (
Problem: 2 a 33 + b 9 ____ 99 if a and b represent positive single digits in the correctly worked computation above , what is the value of a + 3 b ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: adding the digits in unit ' s place , a + 3 + 9 = 19 ( since a and b are positive single digits ) = > a = 7 now adding the digits in ten ' s place , 2 + 3 + b + 1 = 9 ( 1 has been carried over from nit ' s place addition ) = > b = 3 a + 3 b = 2 + 2 * 3 = 11 answer d
Answer: d
Python program:
a = 9 + 2
Problem: if ( 5 - x ) / ( 7 + x ) = x , what is the value of x ^ 2 + 8 x - 5 ?
Options: a ) - 4 , b ) - 3 , c ) - 2 , d ) - 1 , e ) 0
Rationale: "( 5 - x ) = x * ( 7 + x ) ( 5 - x ) = 7 x + x ^ 2 0 = x ^ 2 + 8 x - 5 the answer is e ."
Answer: e
Python program:
a = 5 * 2
b = a - 5
Problem: what percent is 300 gm of 1 kg ?
Options: a ) 25 % , b ) 40 % , c ) 30 % , d ) 8 % , e ) 12 %
Rationale: "1 kg = 1000 gm 300 / 1000 ã — 100 = 30000 / 1000 = 30 % answer is c"
Answer: c
Python program:
a = 300 / 1
b = a * 100
Problem: a man two flats for $ 675958 each . on one he gains 11 % while on the other he loses 11 % . how much does he gain or lose in the whole transaction ?
Options: a ) 1.21 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 11 / 10 ) ^ 2 = 23 / 19 = 1.21 % answer is a"
Answer: a
Python program:
a = 100 + 11 
b = 100 / a
c = b * 675958
d = 100 - 11
e = 100 / d
f = e * 675958
g = c + f 
h = 675958 + 675958 
i = g - h
j = 100 + 11 
k = 100 / j
l = k * 675958
m = 100 - 11
n = 100 / m
o = n * 675958
p = l + o 
q = i / p
r = q * 100
Problem: what is the ratio between perimeters of two squares one having 2 times the diagonal then the other ?
Options: a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 2 : 1 , e ) 3 : 3
Rationale: "d = 2 d d = d a √ 2 = 2 d a √ 2 = d a = 2 d / √ 2 a = d / √ 2 = > 2 : 1 answer : d"
Answer: d
Python program:
a = 2 / 2
b = 2 / a
Problem: richard traveled the entire 60 miles trip . if he did the first 2 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 20 mph , b ) 24 mph , c ) 30 mph , d ) 32 mph , e ) 55 mph
Rationale: average speed = sum of distance / sum of time . if he travelled the first 2 miles at 24 miles / hr , it would take 0.083 hr . for the remaining trip , if he went at 48 miles / 1 hr , it would take 1 hour . then , the average speed is 60 miles / ( 0.083 + 1 ) hrs = 55 miles / 1 hr . therefore , the answer is e .
Answer: e
Python program:
a = 60 - 2
b = a / 48
c = 2 / 24
d = b - c
e = 60 / d
Problem: a man ’ s current age is ( 2 / 5 ) of the age of his father . after 8 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 39
Rationale: a 40 let , father ’ s current age is a years . then , man ’ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 8 ] = ( 1 / 2 ) ( a + 8 ) 2 ( 2 a + 40 ) = 5 ( a + 8 ) a = 40
Answer: a
Python program:
a = 2 / 1
b = 8 * a
c = b - 8
d = 2 / 5
e = 2 / 1
f = d * e
g = 1 - f
h = c / g
Problem: a feed store sells two varieties of birdseed : brand a , which is 60 % millet and 40 % sunflower , and brand b , which is 65 % millet and 35 % safflower . if a customer purchases a mix of the two types of birdseed that is 50 % millet , what percent of the mix is brand a ?
Options: a ) 40 % , b ) 60 % , c ) 50 % , d ) 45 % , e ) 55 %
Rationale: yes there is a simple method : consider the following method brand a : 60 % millet and 40 % sunflower brand b : 65 % millet and 35 % safflower mix : 50 % millet here the weighted average is 50 % , now brand a has 60 % millet , which is 10 % more than the weighted average of mix = + 0.10 a - - - - - - - - - - - - - - - i similarly , brand b has 65 % millet , which is 15 % more than the weighted average of mix = + 0.15 b - - - - - - - - - - - - ii now , both brand a and brand b are combined to give a 50 % mix containing millet , so equate i and ii implies , 0.10 a = 0.15 b therefore a / b = 0.15 / 0.10 = 3 / 2 a : b : ( a + b ) = 3 : 2 : ( 3 + 2 ) = 3 : 2 : 5 we have to find , percent of the mix is brand a i . e . a : ( a + b ) = 3 : 5 = ( 3 / 5 ) * 100 = 60 % here is a pictorial representation : brand a = 60 % - - - - - - - - - - - - - - - - - - - - - - - - 10 % or 0.10 above average , a times - - - - - - - - - - - - - - - - - total above = + 0.10 a - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - average = 50 % or 0.50 brand b = 65 % - - - - - - - - - - - - - - - - - - - - - - - - - - 15 % or 0.15 above average , b times - - - - - - - - - - - - - - - - - total above = + 0.15 b since the amount below the average has to equal the average above the average ; therefore , 0.10 a = 0.15 b a / b = 3 / 2 a : b : total = 3 : 2 : 5 therefore a / total = 3 : 5 = 60 % answer : b
Answer: b
Python program:
a = 3 + 2 
b = 3 / a
c = b * 100
Problem: if the cost price of 30 articles is equal to the selling price of 45 articles , what is the % profit or loss made by the merchant ?
Options: a ) 33.33 % loss , b ) 25 % profit , c ) 20 % loss , d ) 20 % profit , e ) 5 % profit
Rationale: "let the cost price of 1 article be $ 1 . therefore , cost price of 30 articles = 30 * 1 = $ 30 the selling price of 45 articles = cost price of 30 articles = $ 30 . now , we know the selling price of 45 articles . let us find the cost price of 45 articles . cost price of 45 articles = 45 * 1 = $ 45 . therefore , profit made on sale of 45 articles = selling price of 45 articles - cost price of 45 articles = 30 - 45 = - $ 15 . as the profit is in the negative , the merchant has made a loss of $ 15 . therefore , % loss = loss / cp * 100 % loss = - 15 / 45 * 100 = 33.33 % loss . a"
Answer: a
Python program:
a = 100 * 45
b = a / 30
c = 100 - b
d = 100 * 45
e = d / 30
f = c / e
g = 100 * f