euclaise/mathqa_programs huggingface dataset:
Problem: a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 140 , then how much amount should c pay as his share of rent ?
Options: a ) 35 , b ) 45 , c ) 25 , d ) 36 , e ) 55
Rationale: "a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 140 × 9 / 35 = 4 × 9 = 36 answer is d"
Answer: d
Python program:
a = 15 * 3
b = 10 * 7
c = 12 * 5
d = b + c 
e = 15 * 3
f = d + e 
g = a / f
h = 140 * g
Problem: what is the rate percent when the simple interest on rs . 1000 amount to rs . 400 in 4 years ?
Options: a ) 5 % , b ) 6 % , c ) 2 % , d ) 95 % , e ) 10 %
Rationale: "interest for 4 yrs = 400 interest for 1 yr = 100 interest rate = 100 / 1000 x 100 = 10 % answer : e"
Answer: e
Python program:
a = 100 * 400
b = 1000 * 4
c = a / b
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 7 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 9.5 , b ) 9.4 , c ) 9.3 , d ) 9.2 , e ) 9.1
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 7 ) = 3 / 28 the cistern will be filled in 28 / 3 hrs i . e . , 9.3 hrs . answer : c"
Answer: c
Python program:
a = 1 / 4
b = 1 / 7
c = a - b
d = 1 / c
Problem: by how much is 12 % of 24.2 more than 10 % of 14.2 ?
Options: a ) 0.1484 , b ) 14.84 , c ) 1.484 , d ) 2.762 , e ) none
Rationale: "answer required difference = ( 12 x 24.2 ) / 100 - ( 10 x 14.2 ) / 100 = 2.904 - 1.42 = 1.484 . correct option : c"
Answer: c
Python program:
a = 12 / 100
b = 24 * 2
c = 10 / 100
d = c * 14
e = b - d
Problem: the jogging track in a sports complex is 627 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 4.56 min , b ) 5.28 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 627 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 627 m apart , they take ( 100 / 825 * 627 / 1000 ) hrs = ( 627 / 8250 * 60 ) min = 4.56 min . answer : a"
Answer: a
Python program:
a = 627 / 1000
b = 4 + 5 
c = a / b
d = c * const_60
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 27 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 76 sec , b ) 72 sec , c ) 98 sec , d ) 36 sec , e ) 23 sec
Rationale: "speed of train relative to jogger = 27 - 9 = 18 km / hr . = 18 * 5 / 18 = 5 m / sec . distance to be covered = 240 + 120 = 360 m . time taken = 360 / 5 = 72 sec . answer : b"
Answer: b
Python program:
a = 240 + 120 
b = 27 - 9
c = 10 / 2
d = 27 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 36 , what is the total amount ?
Options: a ) 115 , b ) 116 , c ) 117 , d ) 118 , e ) 156
Rationale: "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 36 39 - - - ? = > 156 answer : e"
Answer: e
Python program:
a = 100 / 45
b = a * 36
c = 50 / 45
d = c * 36
e = b + d 
f = e + 36
Problem: a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1989 on her 32 nd birthday first be eligible to retire under this provision ?
Options: a ) 2008 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: "she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1989 + 19 = 2008 . answer : a ."
Answer: a
Python program:
a = 70 - 32
b = a / 2
c = 1989 + b
Problem: carina has 115 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 4 , e ) 3
Rationale: "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 115 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 85 - > y = 105 / 15 . = 7 b"
Answer: b
Python program:
a = 5 * 2
b = 115 - a
c = 10 + 5 
d = b / c
Problem: by weight , liquid x makes up 1.5 percent of solution p and 6.5 percent of solution q . if 400 grams of solution p are mixed with 600 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 3.6 % , b ) 3.9 % , c ) 4.2 % , d ) 4.5 % , e ) 4.8 %
Rationale: "the number of grams of liquid x is 1.5 ( 400 ) / 100 + 6.5 ( 600 ) / 100 = 6 + 39 = 45 grams . 45 / 1000 = 4.5 % the answer is d ."
Answer: d
Python program:
a = 6 * 5
b = a / 100
c = 1 + b 
d = c / 1000
e = d * 100
Problem: a trader bought a car at 40 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 8 % , b ) 62 % , c ) 2 % , d ) 9 % , e ) 22 %
Rationale: "original price = 100 cp = 60 s = 60 * ( 180 / 100 ) = 112 100 - 108 = 8 % answer : a"
Answer: a
Python program:
a = 100 - 40
b = 100 + 80 
c = a * b
d = c / 100
e = d / 100
f = e - 1
g = f * 100
Problem: what is the sum of 100 consecutive integers from - 49 inclusive , in a increasing order ?
Options: a ) - 29 , b ) 50 , c ) - 30 , d ) 30 , e ) 60
Rationale: "from - 49 to - 1 - - > 49 nos . zero - - > 1 number from + 1 to + 49 - - > 49 nos . when we add up nos . from - 49 to + 49 sum will be zero . total 99 nos will be added . 100 th number will be 50 . sum of these 100 nos . = 50 . b is the answer ."
Answer: b
Python program:
a = 49 + 1
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 64 more for rs . 40.00001 , what is reduced price per dozen ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: 40 * ( 40 / 100 ) = 16 - - - 64 ? - - - 12 = > rs . 3 answer : d
Answer: d
Python program:
a = 40 / 100
b = 40 * a
c = b / 64
d = 12 * c
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 24 metre of cloth ?
Options: a ) 175 seconds , b ) 195 seconds , c ) 155 seconds , d ) 188 seconds , e ) 115 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 24 : x = > x = { \ color { blue } \ frac { 24 \ times 1 } { 0.128 } } = > x = 187.5 so time will be approx 188 seconds answer : d"
Answer: d
Python program:
a = 24 / 0
Problem: if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 84 , what is the value of a ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 32 , e ) 42
Rationale: "( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 84 a = 32 the answer is d ."
Answer: d
Python program:
a = 84 * 2
b = 16 - 8
c = a - b
d = 2 + 3 
e = c / d
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 50 paisa and z gets 40 paisa . if the share of x is rs . 30 , what is the total amount ?
Options: a ) 67 , b ) 55 , c ) 62 , d ) 47 , e ) 57
Rationale: "x : y : z = 100 : 50 : 40 10 : 5 : 4 10 - - - 30 19 - - - ? = > 57 answer : e"
Answer: e
Python program:
a = 100 / 50
b = a * 30
c = 40 / 50
d = c * 30
e = b + d 
f = e + 30
Problem: the product of two numbers is 276 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) a ) 29 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35
Rationale: "let the numbers be x and y . then , xy = 276 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 276 ) = 841 x + y = 29 . option a"
Answer: a
Python program:
a = 2 * 276
b = 289 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 276
f = d + e 
g = math.sqrt(f)
Problem: how many kilograms of sugar costing rs . 9 per kg must be mixed with 27 kg of sugar costing rs . 7 per kg so that there may be gain of 10 % by selling the mixture at rs . 9.24 per kg ?
Options: a ) 60 kg , b ) 63 kg , c ) 50 kg , d ) 77 kg , e ) none of these
Rationale: "explanation : let the rate of second quality be rs x per kg . step 1 : s . p of 1 kg of mixture = rs . 9.24 gain = 10 % c . p of 1 kg of mixture = [ 100 / ( 100 + 10 ) × 9.24 ] . = > rs . 8.40 . thus , the mean price = rs . 8.40 . step 2 : c . p of 1 kg of sugar of 1 st kind = 900 p c . p of 1 kg of sugar of 2 nd kind = 700 p mean price = 840 p by the rule of alligation , we have : c . p . of 1 kg of c . p . of 1 kg of sugar of 1 st sugar of 2 nd kind ( 900 p ) kind ( 700 p ) \ / mean price ( 840 p ) / \ 840 - 700 : 900 - 840 ( 140 ) ( 60 ) = > required ratio = 140 : 60 = 7 : 3 . step 3 : let , x kg of sugar of 1 st kind be mixed with 27 kg of 2 nd kind , then = > 7 : 3 = x : 27 . = > 7 / 3 = x / 27 . = > x = ( 7 / 3 ) x 27 . = > x = 63 . answer : b"
Answer: b
Python program:
a = 10 / 100
b = a + 1 
c = 9 / 24
d = 27 * c
e = 27 * 7
f = d - e
g = 10 / 100
h = g + 1 
i = 9 / 24
j = 9 - i
k = f / j
Problem: at a loading dock , each worker on the night crew loaded 1 / 4 as many boxes as each worker on the day crew . if the night crew has 4 / 5 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 6
Rationale: "method : x = no . of boxes loaded by day crew . boxes by night crew = 1 / 4 * 4 / 5 x = 1 / 5 x % loaded by day crew = x / ( x + 1 / 5 x ) = 5 / 6 answer e"
Answer: e
Python program:
a = 5 * 4
b = 5 * 4
c = 1 * 4
d = b + c 
e = a / d
Problem: a train speeds past a pole in 15 seconds and a platform 150 meters long in 25 seconds . what is the length of the train ( in meters ) ?
Options: a ) 205 , b ) 215 , c ) 225 , d ) 235 , e ) 245
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 150 = 25 * ( x / 15 ) 10 x = 2250 x = 225 meters the answer is c ."
Answer: c
Python program:
a = 2 - 1
b = 150 * a
Problem: a jeep takes 7 hours to cover a distance of 420 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 ) 48 kmph , b ) 52 kmph , c ) 40 kmph , d ) 63 kmph , e ) 65 kmph
Rationale: "time = 7 distance = 420 3 / 2 of 7 hours = 7 * 3 / 2 = 10.5 hours required speed = 420 / 10.5 = 40 kmph c )"
Answer: c
Python program:
a = 3 / 2
b = a * 7
c = 420 / b
Problem: the end of a blade on an airplane propeller is 5 feet from the center . if the propeller spins at the rate of 1,320 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet )
Options: a ) 200 π , b ) 240 π , c ) 300 π , d ) 480 π , e ) 150 π
Rationale: "distance traveled in 1 revolution = 2 π r = 2 π 5 / 5280 revolutions in one second = 1320 revolutions in 60 seconds ( one minute ) = 1320 * 60 total distance traveled = total revolutions * distance traveled in one revolution 1320 * 60 * 2 π 5 / 5280 = 150 π e is the answer"
Answer: e
Python program:
a = 2 * 100
b = 2 + 3 
c = b * 1000
d = a + c 
e = 5 / d
f = e * 2
g = 2 * 10
h = 2 + g 
i = 3 + 4 
j = h / i
k = f * j
l = k * 1
m = l * const_60
Problem: what will be the cost of building a fence around a square plot with area equal to 144 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 2784 , b ) 2287 , c ) 2977 , d ) 2668 , e ) 1298
Rationale: "let the side of the square plot be a ft . a 2 = 144 = > a = 12 length of the fence = perimeter of the plot = 4 a = 48 ft . cost of building the fence = 48 * 58 = rs . 2784 . answer : a"
Answer: a
Python program:
a = math.sqrt(144)
b = square_perimeter * (
Problem: what is the 36 th digit to the right of the decimal point in the decimal expansion of 1 / 37 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 7 , e ) 9
Rationale: "1 / 37 = 0.027027 . . . so , we have a repeating cycle of 027 . every third digit ( 3 rd , 6 th , 9 th , . . . ) to the right of the decimal point is 7 , thus 36 th digit to the right of the decimal point is also 7 . answer : d ."
Answer: d
Python program:
a = 1 / 37
Problem: if a ( a - 2 ) = 2 and b ( b - 2 ) = 2 , where a ≠ b , then a + b =
Options: a ) − 1 , b ) − 2 , c ) 4 , d ) 46 , e ) 48
Rationale: "i . e . if a = - 1 then b = 2 or if a = 2 then b = - 1 but in each case a + b = - 1 + 2 = - 1 answer : option a"
Answer: a
Python program:
a = 2 + 2 
b = 2 - 2
c = a + b 
d = c - 1
e = d - 1
f = e - 1
g = f - 1
Problem: if an object travels 400 feet in 4 seconds , what is the object ' s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 68 , b ) 54 , c ) 87 , d ) 96 , e ) 15
Rationale: "1 mile = 5280 feet = > 1 feet = 1 / 5280 miles if the object travels 400 feet in 4 sec then it travels 400 / 4 * 60 * 60 feet in 1 hour ( 1 hr = 60 min * 60 sec ) = 3600 * 100 feet in 1 hour = 360000 feet in 1 hr = 360000 / 5280 miles in 1 hour = 36000 / 528 miles / hr ~ 68 miles / hr answer - a"
Answer: a
Python program:
a = 400 / 5280
b = 1 / 3600
c = 4 * b
d = a / c
Problem: if the sum and difference of two numbers are 10 and 19 respectively , then the difference of their square is :
Options: a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 190
Rationale: let the numbers be x and y . then , x + y = 10 and x - y = 19 x 2 - y 2 = ( x + y ) ( x - y ) = 10 * 19 = 190 . answer : e
Answer: e
Python program:
a = 10 + 19 
b = a / 2
c = b ** 2
d = 10 + 19 
e = d / 2
f = 10 - e
g = f ** 2
h = c - g
Problem: if 14 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 56
Rationale: let x be the number of students in the school . 0.14 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.14 x / 0.25 = 0.56 x students went to the camping which is 56 % . the answer is e
Answer: e
Python program:
a = 100 - 75
b = a / 100
c = 14 / b
Problem: cole drove from home to work at an average speed of 80 kmh . he then returned home at an average speed of 120 kmh . if the round trip took a total of 3 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 85 , e ) 108
Rationale: "first round distance travelled ( say ) = d speed = 80 k / h time taken , t 2 = d / 80 hr second round distance traveled = d ( same distance ) speed = 120 k / h time taken , t 2 = d / 120 hr total time taken = 3 hrs therefore , 3 = d / 80 + d / 120 lcm of 80 and 120 = 240 3 = d / 80 + d / 120 = > 3 = 3 d / 240 + 2 d / 240 = > d = 240 * 2 / 5 km therefore , t 1 = d / 80 = > t 1 = ( 240 * 3 ) / ( 5 x 80 ) = > t 1 = ( 9 x 60 ) / 5 - - in minutes = > t 1 = 108 minutes . e"
Answer: e
Python program:
a = 120 * 3
b = 80 + 120 
c = a / b
d = c * const_60
Problem: the reciprocal of the hcf and lcm of two are 1 / 16 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 208 , e ) 266
Rationale: "reciprocal of the hcf and lcm of two are 1 / 16 and 1 / 312 so , hcf = 16 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 16 * 312 / 24 = 208 answer : d"
Answer: d
Python program:
a = 16 * 312
b = a / 24
Problem: 360 metres long yard , 31 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 17
Rationale: "31 trees have 30 gaps between them , required distance ( 360 / 30 ) = 12 b"
Answer: b
Python program:
a = 31 - 2
b = a + 1 
c = 360 / b
Problem: a test has 120 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 120 . thus 5 c < = 280 and so c < = 56 . then 40 < = c < = 56 and c can have 17 possible values . the answer is d ."
Answer: d
Python program:
a = 120 - 40
b = a / 5
c = b + 1 
d = c + 1
Problem: a = 2 ^ 15 - 625 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get 1 different values and answer is b . . . ."
Answer: b
Python program:
a = 3 * 4
b = 15 - a
Problem: a train running at the speed of 80 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 227 m , b ) 150 m , c ) 187 m , d ) 167 m , e ) 200 m
Rationale: "speed = 80 * 5 / 18 = 200 / 9 m / sec length of the train = speed * time = 200 / 9 * 9 = 200 m answer : e"
Answer: e
Python program:
a = 80 * 1000
b = a / 3600
c = b * 9
Problem: a train 180 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 , b ) 10 , c ) 8 , d ) 2 , e ) 4
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 180 * 3 / 55 = 10 sec . answer b"
Answer: b
Python program:
a = 60 + 6 
b = a * const_0_2778
c = 180 / b
Problem: what is the difference between 38 % of 80 nd 12 % of 160 .
Options: a ) 11.3 , b ) 12.4 , c ) 12.7 , d ) 11.2 , e ) 10.3
Rationale: "( 38 / 100 ) * 80 â € “ ( 12 / 100 ) * 160 30.4 - 19.2 = 11.2 answer : d"
Answer: d
Python program:
a = 38 * 80
b = a / 100
c = 12 * 160
d = c / 100
e = b - d
Problem: paul completes a piece of work in 80 days , rose completes the same work in 120 days . if both of them work together , then the number of days required to complete the work is ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 80 × 120 / 200 = 48 days answer is d
Answer: d
Python program:
a = 1 / 80
b = 1 / 120
c = a + b 
d = 1/(c)
Problem: in a certain pond , 100 fish were caught , tagged , and returned to the pond . a few days later , 100 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 10,000
Rationale: "total fish = x percentage of second catch = ( 2 / 100 ) * 100 = 2 % so , x * 2 % = 50 x = 2500 ans . d"
Answer: d
Python program:
a = 2 / 100
b = 100 / a
Problem: the manufacturing cost of a shoe is rs . 210 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 222 , b ) s 216 , c ) s 258 , d ) s 210 , e ) s 217
Rationale: "explanation : total cost of a watch = 210 + ( 500 / 100 ) = 215 . gain = 20 % = > sp = 1.2 cp = 1.2 x 215 = 258 answer : c"
Answer: c
Python program:
a = 500 / 100
b = 210 + a 
c = 20 / 100
d = 500 / 100
e = 210 + d 
f = c * e
g = b + f
Problem: a vessel of capacity 2 litre has 40 % of alcohol and another vessel of capacity 6 litre had 60 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 44 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
Rationale: "40 % of 2 litres = 0.8 litres 60 % of 6 litres = 3.6 litres therefore , total quantity of alcohol is 4.4 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 44 % b"
Answer: b
Python program:
a = 40 / 100
b = a * 2
c = 60 / 100
d = c * 6
e = b + d 
f = e / 10
g = f * 100
Problem: 65 % of x = 20 % of 422.50 . find the value of x ?
Options: a ) 100 , b ) 130 , c ) 150 , d ) 180 , e ) 199
Rationale: "65 % of x = 20 % of 422.50 then , 65 / 100 * x = 20 / 100 * 4225 / 10 x = 845 / 10 * 100 / 65 = 130 answer is b"
Answer: b
Python program:
a = 422 / 50
b = a * 20
c = b * 100
d = c / 65
Problem: on increasing the number of lines in a page by 80 , they become 240 . what is the % of increase in the no . of lines in the page ?
Options: a ) 20 % , b ) 305 , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: explanation : number of pages increased = 80 now , the number of pages of book = 240 number of pages of the books before increase = 240 – 80 = 160 % increase in the number of pages in the book = 80 160 x 100 % = 50 % c
Answer: c
Python program:
a = 240 - 80
b = 240 / a
c = b * 100
d = c - 100
Problem: a batsman scored 120 runs whichincluded 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets
Options: a ) 40 % , b ) 50 % , c ) 55 % , d ) 65 % , e ) 70 %
Rationale: number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % b
Answer: b
Python program:
a = 3 * 4
b = 3 + 3 
c = b * 8
d = a + c 
e = d / 120
f = e * 100
Problem: in a group of 86 students , each student is registered for at least one of 3 classes – history , math and english . 20 - 8 students are registered for history , 20 - 3 students are registered for math , and forty - 4 students are registered for english . if only 3 students are registered for all 3 classes , how many students are registered for exactly two classes ?
Options: a ) 3 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: a u b u c = a + b + c - ab - bc - ac + abc 86 = 28 + 23 + 44 - ab - bc - ac + 3 = > ab + bc + ac = 12 exactly two classes = ab + bc + ac - 3 abc = 12 - 3 * 3 = 3 hence a
Answer: a
Python program:
a = 20 + 3 
b = 20 + 8 
c = a + b 
d = 4 * 10
e = d + 4 
f = c + e 
g = 3 * 3
h = f - g
i = 86 - 3
j = h - i
Problem: a man can row his boat with the stream at 24 km / h and against the stream in 10 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph
Rationale: "explanation : ds = 24 us = 10 s = ? s = ( 24 - 10 ) / 2 = 7 kmph answer : c"
Answer: c
Python program:
a = 24 - 10
b = a / 2