euclaise/mathqa_programs huggingface dataset:
Problem: two goods trains each 680 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 228 , b ) 65.28 , c ) 48.32 , d ) 27 , e ) 21.1
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 680 + 680 = 1360 m . required time = 1360 * 6 / 125 = 65.28 sec . answer : b"
Answer: b
Python program:
a = 45 + 30
Problem: mike needs 30 % to pass . if he scored 212 marks and falls short by 25 marks , what was the maximum marks he could have got ?
Options: a ) 343 , b ) 677 , c ) 790 , d ) 867 , e ) 932
Rationale: "if mike had scored 25 marks more , he could have scored 30 % therefore , mike required 212 + 25 = 237 marks let the maximum marks be m . then 30 % of m = 237 ( 30 / 100 ) × m = 237 m = ( 237 × 100 ) / 30 m = 23700 / 30 m = 790 answer : c"
Answer: c
Python program:
a = 212 + 25 
b = 30 / 100
c = a / b
Problem: a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 5 or 12 ?
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 30
Rationale: "number of multiples of 5 from 1 through 30 = 30 / 5 = 6 number of multiples of 12 from 1 through 30 = 30 / 12 = 2 number of multiples of 5 and 12 both from 1 through 30 = number of multiples of 12 * 5 ( = 60 ) = 0 total favourable cases = 6 + 2 - 0 = 8 probability = 8 / 30 = 4 / 15 answer : option d"
Answer: d
Python program:
a = 30 / 5
b = math.floor(a)
c = 30 / 12
d = b + c 
e = d / 30
Problem: an aeroplane covers a certain distance of 420 kmph in 6 hours . to cover the same distance in 4 2 / 3 hours , it must travel at a speed of ?
Options: a ) 450 km , b ) 480 km , c ) 500 km , d ) 540 km , e ) 590 km
Rationale: "speed of aeroplane = 420 kmph distance travelled in 6 hours = 420 * 6 = 2520 km speed of aeroplane to acver 2520 km in 14 / 3 = 2520 * 3 / 14 = 540 km answer : option ' d '"
Answer: d
Python program:
a = 420 * 6
b = 3 * 4
c = b + 2 
d = c / 3
e = a / d
Problem: for what value of x between − 5 and 5 , inclusive , is the value of x ^ 2 − 10 x + 16 the greatest ?
Options: a ) − 5 , b ) − 2 , c ) 0 , d ) 2 , e ) 4
Rationale: we can see from the statement that two terms containing x , x ^ 2 will always be positive and - 10 x will be positive if x is - ive . . so the equation will have greatest value if x is - ive , and lower the value of x , greater is the equation . so - 5 will give the greatest value . . ans a
Answer: a
Python program:
a = negate ** (
b = a + 2 
c = b - 16
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 15 % ?
Options: a ) 20 % , b ) 27.5 % , c ) 10 % , d ) 80 % , e ) 90 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 85 2 / 3 sp 1 = 85 sp 1 = 127.5 100 - - - 27.5 = > 27.5 % answer : b"
Answer: b
Python program:
a = 100 - 15
b = 2 / 3
c = a / b
d = c - 100
Problem: a boat running up stram takes 5 hours to cover a certain distance , while it takes 8 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ?
Options: a ) 2 : 3 , b ) 5 : 6 , c ) 4 : 5 , d ) 7 : 1 , e ) 13 : 3
Rationale: "explanation : let speed of boat is x km / h and speed stream is y km / hr 5 ( x + y ) = 8 ( x - y ) 5 x + 5 y = 8 x - 8 y 13 y = 3 x x / y = 13 / 3 13 : 3 answer : option e"
Answer: e
Python program:
a = 8 - 5
Problem: machine p and machine q are each used to manufacture 880 sprockets . it takes machine p 10 hours longer to produce 880 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 880 / x = 880 / 1.1 x + 10 1.1 ( 880 ) = 880 + 11 x 11 x = 88 x = 8 the answer is d ."
Answer: d
Python program:
a = 10 / 100
b = a + 1 
c = 880 / b
d = 880 - c
e = d / 10
Problem: in an examination 35 % of the students passed and 351 failed . how many students appeared for the examination ?
Options: a ) a ) 540 , b ) b ) 400 , c ) c ) 700 , d ) d ) 650 , e ) e ) 840
Rationale: let the number of students appeared be x then , 65 % of x = 351 65 x / 100 = 351 x = 351 * 100 / 65 = 540 answer is a
Answer: a
Python program:
a = 351 * 100
b = 100 - 35
c = a / b
Problem: what is the average of 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , and 1200 ?
Options: a ) 1360.47 , b ) 1355.8 , c ) 1380 , d ) 1350 , e ) 1333
Rationale: add 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , and 1200 grouping numbers together may quicken the addition sum = 9660 9660 / 7 = 1380 c
Answer: c
Python program:
a = 1200 + 1300 
b = a + 1400 
c = b + 1510 
d = c + 1520 
e = d + 1530 
f = e + 1200 
g = 3 + 4 
h = f / g
Problem: if w is 40 percent less than q , q is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ?
Options: a ) 4 % , b ) 18 % , c ) 36 % , d ) 40 % , e ) 50 %
Rationale: given w = 0.6 q , q = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer .
Answer: e
Python program:
a = 100 - 46
b = 100 - 40
c = 100 - 40
d = 40 * c
e = d / 100
f = b - e
g = a - f
h = 100 - 40
i = 100 - 40
j = 40 * i
k = j / 100
l = h - k
m = g / l
n = m * 100
Problem: a man rows his boat 70 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 1 kmph , b ) 6 kmph , c ) 5 kmph , d ) 8 kmph , e ) 7 kmph
Rationale: "speed downstream = d / t = 75 / ( 2 1 / 2 ) = 28 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 28 - 18 ) / 2 = 5 kmph answer : c"
Answer: c
Python program:
a = const_60 / 0
b = 45 / 2
c = a - b
d = c / 2
Problem: a train passes a station platform in 48 sec and a man standing on the platform in 40 sec . if the speed of the train is 36 km / hr . what is the length of the platform ?
Options: a ) 80 , b ) 120 , c ) 60 , d ) 90 , e ) 50
Rationale: "speed = 36 * 5 / 18 = 10 m / sec . length of the train = 10 * 40 = 400 m . let the length of the platform be x m . then , ( x + 400 ) / 48 = 10 = > x = 80 m . answer : a"
Answer: a
Python program:
a = 36 * const_0_2778
b = 40 * a
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 12 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 32 % , c ) 35 % , d ) 37.5 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.88 * 150 x = 132 x hence total profit = 32 % option b"
Answer: b
Python program:
a = 100 - 12
b = a / 100
c = 100 + 20 
d = 100 + 25 
e = d / 100
f = c * e
g = b * f
h = g - 100
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18600 . a ' s share is ?
Options: a ) 8876 , b ) 2765 , c ) 6000 , d ) 6200 , e ) 1261
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18600 = 6200 answer : d"
Answer: d
Python program:
a = 1 * 12
b = 1 * 12
c = 12 - 6
d = c * 2
e = b + d 
f = 12 - 8
g = f * 3
h = e + g 
i = 18600 / h
j = a * i
Problem: a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 5 : 6 : 7 : 8 : 9 . in all papers together , the candidate obtained 60 % of the total marks . then the number of papers in which he got more than 50 % marks is
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 1
Rationale: here we can assume that one subject is of 100 marks so total there are 5 subjects = > 100 * 5 = 500 . now according to the question he secured 60 % of those which is 60 % of 500 = 300 marks in total . the ratio between the marks is given as 5 : 6 : 7 : 8 : 9 , so now we can distribute 300 marks according to the ratio . total ratio = 35 for 6 : ( 300 / 35 ) * 6 = 51.4 similarly , we will get for others as 60 , 68.57 , 77.14 hence , there are 5 subject where he secured more that 50 % . the answer is 5 . d
Answer: d
Python program:
a = 1 + 4
Problem: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 6 ¤ √ 6 =
Options: a ) 0 , b ) 5 , c ) 10 , d ) 24 , e ) 20
Rationale: "x = √ 6 and y also = √ 6 applying the function ( √ 6 + √ 6 ) ^ 2 - ( √ 6 - √ 6 ) ^ 2 = ( 2 √ 6 ) ^ 2 - 0 = 4 x 6 = 24 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 6 and y = √ 6 you get the answer 24 . answer d"
Answer: d
Python program:
a = math.sqrt(6)
b = math.sqrt(6)
c = a + b 
d = c ** 2
Problem: an investment yields an interest payment of $ 240 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ?
Options: a ) $ 28,300 , b ) $ 30,400 , c ) $ 31,300 , d ) $ 32,500 , e ) $ 32,000
Rationale: "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 240 = > p = ( 240 * 4 * 10 ^ 2 ) / 3 = 80 * 4 * 10 ^ 2 = 320 * 10 ^ 2 = 32000 answer e"
Answer: e
Python program:
a = 3 * 4
b = 9 / a
c = 240 / b
d = c * 100
Problem: the inner circumference of a circular race track , 14 m wide , is 440 m . find radius of the outer circle ?
Options: a ) 22 , b ) 37 , c ) 87 , d ) 84 , e ) 82
Rationale: "let inner radius be r metres . then , 2 r = 440 ; r = = 70 m . radius of outer circle = ( 70 + 14 ) m = 84 m . answer : d"
Answer: d
Python program:
a = 440 / math.pi
b = a / 2
c = 14 + b
Problem: the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 25 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 400 km , b ) 500 km , c ) 331.2 km , d ) 550 km , e ) 600 km
Rationale: "sol . average speed of a tractor = 23 km / h the speed of a bus in an hour = 23 × 2 = 46 km the speed of a car in an hour = 9 / 5 * 46 = 82.8 km so , the distance covered by car in 4 h is 82.8 × 4 = 331.2 km ans . ( c )"
Answer: c
Python program:
a = 4 / 5
b = 1 + a 
c = 575 / 25
d = 2 * c
e = b * d
f = e * 4
Problem: there are 56 lights which are functional and each is controlled by a separate on / off switch . two children x and y start playing with the switches . x starts by pressing every third switch till he reaches the end . y , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 18 , b ) 19 , c ) 17 , d ) 15 , e ) 16
Rationale: editing my solution : number of switches = 56 number of switches turned on by x : 3 , 6 , . . . 54 = 18 number of switches turned on by y : 5 , 10 , . . . . 55 = 11 few switches are turned on by x and later turned off by y : lcm ( 35 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both x and y as they are turned off . number of switches that are turned on = ( 18 - 6 ) + ( 11 - 6 ) = 17 answer : c
Answer: c
Python program:
a = 4 * 10
b = 56 - a
c = b + 1
Problem: how many multiples of 5 are there between 5 to 95 ?
Options: a ) 9 , b ) 18 , c ) 17 , d ) 16 , e ) 15
Rationale: "as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the unit ’ s place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 , 85 , 90 . answer c"
Answer: c
Python program:
a = 95 - 5
b = a / 5
c = b + 1
Problem: the difference between the local value and face value of 7 in the numeral 657903 is :
Options: a ) 0 , b ) 7896 , c ) 6993 , d ) 903 , e ) 803
Rationale: ( local value ) - ( face value ) = ( 7000 - 7 ) = 6993 . answer : c
Answer: c
Python program:
a = 7 * 1000
b = a - 7
Problem: find the value of b from ( 15 ) ^ 2 x 9 ^ 2 ã · 356 = b .
Options: a ) 53.2 , b ) 52.2 , c ) 51.2 , d ) 8.2 , e ) 54.2
Rationale: given exp . = ( 15 ) ^ 2 x 9 ^ 2 ã · 356 = b = 225 x 81 ã · 356 = 51.2 c
Answer: c
Python program:
a = 15 ** 2
b = 9 ** 2
c = a * b
d = c / 356
Problem: an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 1 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 4 : 5 , b ) 9 : 10 , c ) 14 : 15 , d ) 19 : 20 , e ) 24 : 25
Rationale: "let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be y and y . 2 ( 3 x + 2 x ) = 2 ( y + y ) 5 x = 2 y ( 5 / 2 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : y * y = 6 x ^ 2 : y ^ 2 = 6 x ^ 2 : ( 25 / 4 ) * x ^ 2 = 24 : 25 the answer is e ."
Answer: e
Python program:
a = rectangle_area / (
Problem: how many cuboids of length 5 m , width 2 m and height 3 m can be farmed from a cuboid of 18 m length , 15 m width and 2 m height .
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "( 18 ã — 15 ã — 12 ) / ( 5 ã — 3 ã — 2 ) = 18 answer is e ."
Answer: e
Python program:
a = 18 * 15
b = a * 2
c = 5 * 2
d = c * 3
e = b / d
Problem: an engineer undertakes a project to build a road 10 km long in 60 days and employs 30 men for the purpose . after 20 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) 20 , b ) 15 , c ) 30 , d ) 45 , e ) 60
Rationale: "30 workers working already let x be the total men required to finish the task in next 40 days 2 km done hence remaining is 8 km also , work has to be completed in next 40 days ( 60 - 20 = 40 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 20 ) / ( 2 * 40 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : c"
Answer: c
Python program:
a = 10 - 2
b = 30 * a
c = b * 20
d = 60 - 20
e = 2 * d
f = c / e
g = f - 30
Problem: a retailer bought a machine at a wholesale price of $ 81 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 108 , c ) 120 , d ) 135 , e ) 160
Rationale: "my solution : wholesale price = 81 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 81 + 1 / 5 ( 81 ) x = 108 ; answer : b"
Answer: b
Python program:
a = 81 * 20
b = a / 100
c = 81 + b 
d = c * 100
e = 3 * 3
f = e * 10
g = d / f
Problem: 1.5 , 2.3 , 3.1 , 3.9 , . . ?
Options: a ) 0.6 , b ) 0.8 , c ) 0.4 , d ) 0.24 , e ) 0.15
Rationale: "1.5 + 0.8 = 2.3 2.3 + 0.8 = 3.1 3.1 + 0.8 = 3.9 3.9 + 0.8 = 4.7 answer : b"
Answer: b
Python program:
a = negate - (
Problem: at steel factory , each employee working the second shift produced 2 / 3 as many widgets as each employee working the first shift . if the first shift has 3 / 4 as many employees , what fraction of the total widgets did the second shift produce ?
Options: a ) 8 / 17 , b ) 1 / 2 , c ) 8 / 9 , d ) 9 / 8 , e ) 17 / 8
Rationale: at steel factory , let the first shift have 3 employee and each produce 3 widgets , so the total number of widgets produced by the first shift is 3 * 3 = 9 ; then the second shift would have 4 employees and each second shift employee would produce 3 * 2 / 3 = 2 widgets , so the total number of widgets produced by the second shift employees would be 4 * 2 = 8 ; the ratio of the second shift production to the total is 8 / ( 9 + 8 ) = 8 / 17 . answer : a .
Answer: a
Python program:
a = 2 / 3
b = a * 4
c = 2 / 3
d = c * 4
e = 3 + d 
f = b / e
Problem: a circular swimming pool is surrounded by a concrete wall 4 ft wide . if the area of the concrete wall surrounding the pool is 11 / 25 that of the pool , then the radius of the pool is ?
Options: a ) 22 , b ) 20 , c ) 88 , d ) 387 , e ) 19
Rationale: "let the radius of the pool be rft radius of the pool including the wall = ( r + 4 ) ft area of the concrete wall = { \ color { black } \ pi \ left [ ( r + 4 ) ^ { 2 } - r ^ { 2 } \ right ] } = { \ color { black } \ pi \ left [ ( r + 4 + r ) ( r + 4 - r ) \ right ] = 8 \ pi ( r + 2 ) } sq feet { \ color { black } \ rightarrow 8 \ pi ( r + 2 ) = \ frac { 11 } { 25 } \ pi r ^ { 2 } \ rightarrow 11 r ^ { 2 } = 200 ( r + 2 ) } radius of the pool r = 20 ft answer : b ) 20 ft"
Answer: b
Python program:
a = 2 * 4
b = 2 * 4
c = b ** 2
d = 11 / 25
e = d * 4
f = 4 ** 2
g = e * f
h = c + g 
i = math.sqrt(h)
j = a + i 
k = 11 / 25
l = j / k
m = l / 2
Problem: 36 men can complete a piece of work in 18 days . in how many days will 81 men complete the same work ?
Options: a ) 8 , b ) 77 , c ) 88 , d ) 29 , e ) 21
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 81 : 36 : : 18 : x x = 8 answer : a ) 8 days"
Answer: a
Python program:
a = 18 * 36
b = a / 81
Problem: simplify : 0.2 * 0.4 + 0.6 * 0.8
Options: a ) 0.52 , b ) 0.42 , c ) 0.48 , d ) 0.64 , e ) 0.56
Rationale: "given exp . = 0.2 * 0.4 + ( 0.6 * 0.8 ) = 0.08 + 0.48 = 0.56 answer is e ."
Answer: e
Python program:
a = 0 * 2
b = 0 * 6
c = a + b
Problem: what is 0.05 percent of 12,356 ?
Options: a ) 0.6178 , b ) 61.78 , c ) 6.178 , d ) 0.06178 , e ) 0.006178
Rationale: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.05 ( 1 / 100 ) 12,356 . the answer is 6.178 . hence , the correct answer is c .
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 0 * 5
p = o / 100
Problem: 15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container s ?
Options: a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42
Rationale: "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ."
Answer: c
Python program:
a = 9 + 16 
b = 9 / a
c = math.sqrt(b)
d = 1 - c
e = 15 / d
Problem: a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio e of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: "he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore e , w _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b"
Answer: b
Python program:
a = 3 + 2 
b = 3 / a
c = 20 - 10
d = b * c
e = d + 10 
f = e / 20
g = 20 - 10
h = f * g
i = h + 10 
j = 3 + 2 
k = 2 / j
l = 20 - 10
m = k * l
n = m / 20
o = 20 - 10
p = n * o
q = i / p
Problem: an article is bought for rs . 800 and sold for rs . 1200 , find the loss percent ?
Options: a ) 55 % , b ) 25.25 % , c ) 33.33 % , d ) 45 % , e ) 50 %
Rationale: "800 - - - - 400 400 - - - - ? = > 50 % answer : e"
Answer: e
Python program:
a = 1200 * 100
b = a / 800
c = 100 - b
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 $ 0.50 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 ) $ 1,250 , e ) $ 2,550
Rationale: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.5 = $ 255 answer a"
Answer: a
Python program:
a = 1000 * 1000
b = 3 * 6
c = 20 * 20
d = c * 15
e = b / d
f = e * 0
Problem: diana works 10 hours per day on monday , wednesday and friday , and 15 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 1800 per week . how much does she earn in dollars per hour ?
Options: a ) 20 , b ) 22 , c ) 30 , d ) 24 , e ) 25
Rationale: so , she works 30 hours in 3 days so , she works 30 hours in 2 days so in a week she works 60 hours ( 30 + 30 ) and earns $ 1800 so , hourly wage is 1800 / 60 = > 30 hence answer will be ( c ) 30
Answer: c
Python program:
a = 2 * 15
b = 10 * 3
c = a + b 
d = 1800 / c
Problem: a car travels at a speed of 65 miles per hour . how far will it travel in 8 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 520 miles , d ) 425 miles , e ) 525 miles
Rationale: "during each hour , the car travels 65 miles . for 8 hours it will travel 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 = 8 × 65 = 520 miles correct answer is c ) 520 miles"
Answer: c
Python program:
a = 65 * 8
Problem: the mean of 50 observations was 36 . it was found later that an observation 30 was wrongly taken as 23 . the corrected new mean is :
Options: a ) 36.02 , b ) 36.14 , c ) 36.12 , d ) 36.11 , e ) 36.8
Rationale: explanation : correct sum = ( 36 * 50 + 30 - 23 ) = 1825 . correct mean = = 1807 / 50 = 36.14 answer : b ) 36.14
Answer: b
Python program:
a = 36 * 50
b = 50 - 2
c = b - 23
d = a + c 
e = d / 50