euclaise/mathqa_programs huggingface dataset:
Problem: bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 56 more . what was his original selling price ?
Options: a ) $ 880 , b ) $ 950 , c ) $ 1100 , d ) $ 1240 , e ) $ 1360
Rationale: "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 56 0.07 = 56 p = 800 the original selling price was 800 * 1.1 = 880 . the correct answer is a ."
Answer: a
Python program:
a = 10 / 100
b = 1 - a
c = 30 / 100
d = 1 + c 
e = b * d
f = 10 / 100
g = 1 + f 
h = e - g
i = 56 / h
j = 10 / 100
k = 1 + j 
l = i * k
Problem: a train speeds past a pole in 10 seconds and a platform 100 m long in 30 seconds . its length is ?
Options: a ) 188 m , b ) 876 m , c ) 251 m , d ) 50 m , e ) 45 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 10 = > y = x / 10 x + 100 / 30 = x / 10 x = 50 m . answer : d"
Answer: d
Python program:
a = 2 - 1
b = 100 * a
Problem: suraj has a certain average of runs for 16 innings . in the 17 th innings he scores 112 runs thereby increasing his average by 6 runs . what is his average after the 17 th innings ?
Options: a ) 18 , b ) 25 , c ) 16 , d ) 72 , e ) 27
Rationale: "to improve his average by 6 runs per innings he has to contribute 16 x 6 = 96 runs for the previous 16 innings . thus , the average after the 17 th innings = 112 - 96 = 16 . answer : c"
Answer: c
Python program:
a = 16 * 6
b = 112 - a
c = 17 - 16
d = b / c
Problem: a man can row downstream at the rate of 16 km / hr and upstream at 8 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 12,4 , b ) 6,3 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 16 + 8 ) = 12 km / hr rate of current = 1 / 2 ( 16 - 8 ) = 4 km / hr answer : option a"
Answer: a
Python program:
a = 16 - 8
b = a / 2
Problem: the average of squares of first 11 consecutive even numbers is :
Options: a ) 164 , b ) 174 , c ) 184 , d ) 194 , e ) 204
Rationale: 2 ( n + 1 ) ( 2 n + 1 ) / 3 ( 2 * 12 * 23 ) / 3 = 2 * 4 * 23 = 184 answer : c
Answer: c
Python program:
a = 11 + 1 
b = 2 * a
c = 11 * 2
d = c + 1 
e = b * d
f = e / 3
Problem: the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1430 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 190 , d ) 321 , e ) 220
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1430 x = 50 required perimeter = 2 ( 50 + 60 ) = 220 e"
Answer: e
Python program:
a = 1430 / 6
b = a / 2
c = b - 10
d = c / 2
e = 1430 / 6
f = e / 2
g = f - 10
h = g / 2
i = h + 10 
j = d + i 
k = j * 2
Problem: rahul played weel in this season . his current batting averagge is 51 . if he score 69 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: 51 x + 69 = 54 ( x + 1 ) = > 3 x = 15 = > x = 5 answer : e
Answer: e
Python program:
a = 69 - 54
b = 54 - 51
c = a / b
Problem: 1852 - 1230 ÷ 10.00 = ?
Options: a ) 62.2 , b ) 2000 , c ) 1700 , d ) 1729 , e ) none
Rationale: "answer given expression = 1852 - 1230 ÷ 10.00 = 1852 - 123 = 1729 correct option : d"
Answer: d
Python program:
a = 1852 / 100
b = a * 1230
c = 1 / 3
d = 1852 / 100
e = d * 1230
f = c * e
g = b - f
Problem: last year a certain bond price with a face value of 5000 yielded 8 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 4063 , b ) 5325 , c ) 5351 , d ) 6000 , e ) 6154
Rationale: "interest = 0.08 * 5000 = 0.065 * selling price - - > selling price = 0.08 * 5000 / 0.065 - - > selling price = ~ 6,154 answer : e ."
Answer: e
Python program:
a = 8 / 100
b = 5000 * a
c = 6 / 5
d = b / c
Problem: mixture contains alcohol and water in the ratio 4 : 3 . if 8 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 99 , c ) 27 , d ) 4 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 32 x = 4 ( 3 x + 5 ) 20 x = 20 x = 1 quantity of alcohol = ( 4 x 1 ) litres = 4 litres . answer : d"
Answer: d
Python program:
a = 4 * 5
b = 8 * 4
c = 3 * 4
d = b - c
e = a / d
f = e * 4
Problem: mary ' s income is 60 % more than tim ' s income and tim ' s income is 50 % less than juan ' s income . what % of juan ' s income is mary ' s income .
Options: a ) 124 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "even i got 96 % j = 100 t = 100 * 0.5 = 50 m = 50 * 1.6 = 80 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 80 * 100 / 100 = 80 ans : d"
Answer: d
Python program:
a = 100 - 50
b = 100 - 50
c = 60 / 100
d = b * c
e = a + d
Problem: laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 40 kmph and prasanna moves southward at a speed of 38 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 11 , b ) 50 , c ) 78 , d ) 27 , e ) 18
Rationale: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 40 kmph x 1 hr = 40 km total southward prasanna ' s distance = 38 kmph x 1 hr = 38 km total distance between prasanna and laxmi is = 40 + 38 = 78 km . answer : c"
Answer: c
Python program:
a = 40 + 38
Problem: a grocer has 400 pounds of coffee in stock , 20 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 70 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 36 %
Rationale: "1 . 20 % of 400 = 80 pounds of decaffeinated coffee 2 . 70 % of 100 = 70 pounds of decaffeinated coffee 3 . wt have 150 pounds of decaffeinated out of 500 pounds , that means 150 / 500 * 100 % = 30 % . the correct answer is b ."
Answer: b
Python program:
a = 20 / 100
b = a * 400
c = 70 / 100
d = 100 * c
e = b + d 
f = 400 + 100 
g = e / f
h = g * 100
Problem: the value of ( 34.31 * 0.5 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.05 , d ) 2.27 , e ) 2.35
Rationale: "( 34.31 * 0.5 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) = 26.882 / 11.845 = 2.27 answer : d"
Answer: d
Python program:
a = 34 * 31
b = a * 1
c = 7 * 57
d = c * 0
e = b / d
f = e / 10
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 11 years , c ) 14 years , d ) 21 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 5 + 16 x 9 ) ] = ( 225 - 214 ) = 11 years . answer b"
Answer: b
Python program:
a = 15 * 15
b = 5 * 14
c = 9 * 16
d = b + c 
e = a - d
Problem: the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 14300 , b ) 14400 , c ) 14500 , d ) 14600 , e ) 15400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 × 120 / 100 = 14400 b )"
Answer: b
Python program:
a = 10000 * 20
b = a / 100
c = b * 2
d = 10000 + c
Problem: what is the decimal equivalent of ( 1 / 4 ) ^ 3 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.0156
Rationale: ( 1 / 4 ) ^ 3 = 1 / 64 = 0.0156 answer : e
Answer: e
Python program:
a = 1 / 4
b = a ** 3
Problem: a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 40 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 72.72 , e ) 97.2
Rationale: "let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 40 * 5 = 200 student ' s average = ( 600 + 200 ) / 11 = 72.72 answer d"
Answer: d
Python program:
a = 6 * 100
b = 5 * 40
c = a + b 
d = 6 + 5 
e = c / d
f = math.floor(e)
Problem: at what price must an article costing rs . 66.5 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 87.5 , b ) 89.5 , c ) 82.3 , d ) 82.1 , e ) 92.4
Rationale: "cp = 66.5 sp = 66.5 * ( 125 / 100 ) = 83.125 mp * ( 95 / 100 ) = 59.375 mp = 87.5 answer : a"
Answer: a
Python program:
a = 66 * 5
b = a / 100
c = 66 + 5 
d = c * 100
e = 100 - 5
f = d / e
Problem: three 6 faced dice are thrown together . the probability that all the three show the same number on them is - .
Options: a ) 1 / 36 , b ) 1 / 216 , c ) 1 / 48 , d ) 1 / 55 , e ) 1 / 90
Rationale: "it all 3 numbers have to be same basically we want triplets . 111 , 222 , 333 , 444 , 555 and 666 . those are six in number . further the three dice can fall in 6 * 6 * 6 = 216 ways . hence the probability is 6 / 216 = 1 / 36 answer a"
Answer: a
Python program:
a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
Problem: the smallest number which when diminished by 7 , is divisible 12 , 16 , 18 , 21 and 28 is :
Options: a ) 1008 , b ) 1015 , c ) 1022 , d ) 1032 , e ) none of these
Rationale: "explanation required number = ( l . c . m . of 12,16 , 18 , 21 , 28 ) + 7 = 1008 + 7 = 1015 answer b"
Answer: b
Python program:
a = 3 ** 2
b = 2 ** 0
c = a * b
d = 3 + 4 
e = c * d
f = e + 7
Problem: the average of first 15 even numbers is ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 16 , e ) 14
Rationale: "sum of 15 even numbers = 15 * 16 = 240 average = 240 / 15 = 16 answer : d"
Answer: d
Python program:
a = 15 + 1
Problem: in 100 litres mixture milk and water are in the ratio 3 : 2 . after adding how many liters of water its ratio will become 3 : 4
Options: a ) 48 , b ) 50 , c ) 62 , d ) 78 , e ) 100
Rationale: milk quantity = 3 / 5 * 60 = 36 water quantity = 100 - 36 = 64 new ratio of m : w = 36 : 64 + x = 3 : 4 192 + 3 x = 144 x = 48 answer is a
Answer: a
Python program:
a = 3 + 2 
b = 3 / a
c = b * 100
d = 3 + 4 
e = 3 / d
f = c / e
g = f - 100
h = 10 + 2 
i = h / 10
j = g * i
Problem: a sum fetched a total simple interest of 4034.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 5768 , b ) 8925 , c ) 8965 , d ) 6474 , e ) 8723
Rationale: "principal = ( 100 x 4034.25 ) / ( 9 x 5 ) = 403425 / 45 = 8965 . answer c"
Answer: c
Python program:
a = 4034 * 25
b = a / 9
c = b / 5
Problem: rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage w .
Options: a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %
Rationale: "given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % w = ( 97 / 556 ) * 100 = 17.4 % answer : b"
Answer: b
Python program:
a = 2 * 10
b = 2 * 10
c = b + 1 
d = a * c
e = 25 / 100
f = e + 1 
g = 10 / f
h = 15 + 2 
i = g * h
j = d + i 
k = 653 - j
l = 2 * 10
m = 2 * 10
n = m + 1 
o = l * n
p = 25 / 100
q = p + 1 
r = 10 / q
s = 15 + 2 
t = r * s
u = o + t 
v = k / u
w = v * 100
Problem: cereal a is 9 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 5 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
Rationale: "( 9 / 100 ) a + ( 2 / 100 ) b = ( 4 / 100 ) ( a + b ) 5 a = 2 b = > a / b = 2 / 5 answer is b ."
Answer: b
Python program:
a = 4 - 2
b = 9 - 4
c = a / b
Problem: how long does a train 180 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?
Options: a ) 33 , b ) 56 , c ) 55 , d ) 82 , e ) 62
Rationale: "explanation : t = ( 660 + 180 ) / 54 * 18 / 5 t = 56 answer : option b"
Answer: b
Python program:
a = 180 + 660 
b = 54 * const_0_2778
c = a / b
Problem: a profit of rs . 500 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) rs . 200 , b ) rs . 100 , c ) rs . 300 , d ) rs . 50 , e ) rs . 90
Rationale: "a profit of rs . 500 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 300 and 200 . difference in profit share = 300 - 200 = 100 answer : b"
Answer: b
Python program:
a = 1 / 2
b = 1 / 3
c = a + b 
d = 500 / c
e = d / 2
f = 1 / 2
g = 1 / 3
h = f + g 
i = 500 / h
j = i / 3
k = e - j
Problem: a man buys rs . 56 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 42
Rationale: "dividend on rs . 56 = rs . 9 / 100 x 56 = rs . 5.04 . rs . 12 is an income on rs . 100 . rs . 5.04 is an income on rs . 100 / 12 x 5.04 = rs . 42 . answer : option e"
Answer: e
Python program:
a = 100 / 12
b = 9 / 100
c = b * 56
d = a * c
Problem: of 440 surveyed students , 20 % of those who read book a also read book b and 25 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 55
Rationale: "say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 440 = 1.25 b + b - 0.25 b - - > b = 220 , a = 1.25 b = 275 and { both } = 0.25 b = 55 . the number of students who read only book a is { a } - { both } = 125 - 25 = 100 ; the number of students who read only book b is { b } - { both } = 275 - 55 - 220 ; the difference is 220 - 55 = 165 . answer : e ."
Answer: e
Python program:
a = 25 / 100
b = 20 / 100
c = a / b
d = c + 1 
e = 25 / 100
f = d - e
g = 440 / f
h = 25 / 100
i = 20 / 100
j = h / i
k = g * j
l = 20 / 100
m = 1 - l
n = k * m
o = 25 / 100
p = 20 / 100
q = o / p
r = q + 1 
s = 25 / 100
t = r - s
u = 440 / t
v = 25 / 100
w = 1 - v
x = u * w
y = n - x
Problem: on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 30 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 14.3 % , d ) 22 % , e ) 30 %
Rationale: "suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 30 % of y exceeded the speed limit but did n ' t received the ticket , i . e . 3 y / 10 . it means 7 y / 10 received the ticket . hence , 7 y / 10 = x / 10 or y / x = 1 / 7 or y / x * 100 = 1 / 7 * 100 = 14.3 % c"
Answer: c
Python program:
a = 100 - 30
b = 10 / a
c = b * 100
Problem: ajay can ride 50 km in 1 hour . in how many hours he can ride 750 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: "1 hour he ride 50 km he ride 750 km in = 750 / 50 * 1 = 15 hours answer is b"
Answer: b
Python program:
a = 750 / 50
Problem: a number of 47 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 17
Rationale: "to maximize # of boxes we should minimize marbles per box : 14 * 3 + 1 * 5 = 47 - - > 14 + 1 = 15 . answer : c ."
Answer: c
Python program:
a = 47 / 3
Problem: 12 is subtracted from 95 % of a number , the result is 178 . find the number ?
Options: a ) 200 , b ) 240 , c ) 198 , d ) 190 , e ) 322
Rationale: "( 95 / 100 ) * x â € “ 12 = 178 9.5 x = 1900 x = 200 answer : a"
Answer: a
Python program:
a = 12 + 178 
b = 95 / 100
c = a / b
Problem: a man invests rs . 8000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 4000 , e ) none of these
Rationale: explanation : interest on rs . 8000 at 5 % per annum = ( 8000 × 5 × 1 ) / 100 = rs . 400 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 8000 + x ) × 6 × 1 / 100 . = > 400 + 2 x / 25 = ( 8000 + x ) × 6 × 1 / 100 . = > 40000 + 8 x = ( 8000 + x ) × 6 . = > 40000 + 8 x = 48000 + 6 x . = > 2 x = 8000 . = > x = 4000 . answer : d
Answer: d
Python program:
a = 8000 * 6
b = 8000 * 5
c = a - b
d = 8 - 6
e = c / d
Problem: the cost per unit of electricity during a 4 year period is as follows : year 1 , $ 3 per unit ; year 2 , $ 4 per unit ; year 3 , $ 5 per unit ; year 4 , $ 6 per unit . if a factory spent equal dollars on electricity each year , what was the average cost of a unit of electricity during the 4 year period ?
Options: a ) $ 4.31 , b ) $ 4.51 , c ) $ 4.21 , d ) $ 5.21 , e ) $ 5.61
Rationale: let money spent each year = $ 60 units bought first year = 20 units bought second year = 15 units bought third year = 12 units bought fourth year = 10 total number of units = 57 total money spent = 60 * 4 = 240 average = 240 / 57 = 4.21 answer : c
Answer: c
Python program:
a = 1 / 3
b = 1 / 4
c = a + b 
d = 1 / 5
e = c + d 
f = 1 / 6
g = e + f 
h = 4 / g
Problem: in what time will a train 45 m long cross an electric pole , it its speed be 108 km / hr ?
Options: a ) 0.5 , b ) 1.25 , c ) 1.5 , d ) 2.5 , e ) 3.5
Rationale: "speed = 108 * 5 / 18 = 30 m / sec time taken = 45 / 30 = 1.5 sec . answer : c"
Answer: c
Python program:
a = 108 * const_0_2778
b = 45 / a
Problem: in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 10 of the housing units , including 1 / 4 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?
Options: a ) 3 / 4 , b ) 11 / 15 , c ) 7 / 10 , d ) 1 / 6 , e ) 2 / 15
Rationale: 1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 4 ( equiped with cable tv ) i . e . 1 / 4 ( 1 / 5 ) = 1 / 20 therefore only video cassette recorder = 1 / 10 - 1 / 20 = 1 / 20 total = 1 / 5 + 1 / 20 + neither cable tv nor videocassette recorders 1 = 1 / 4 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 1 / 4 = 3 / 4 hence a .
Answer: a
Python program:
a = 10 + 5 
b = 10 * 2
c = a / b
Problem: two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 45 sec . the length of each train is ?
Options: a ) 50 , b ) 26 , c ) 27 , d ) 62.5 , e ) 21
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 45 = 25 / 9 = > x = 65.5 . answer : d"
Answer: d
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = 45 * c
e = d / 2
Problem: a batsman makes a score of 87 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options: a ) 19 , b ) 29 , c ) 39 , d ) 49 , e ) 59
Rationale: "solution let the average after 17 th inning = x . then , average after 16 th inning = ( x - 3 ) average = 16 ( x - 3 ) + 87 = 17 x or x = ( 87 - 48 ) = 39 . answer c"
Answer: c
Python program:
a = 17 * 3
b = 87 - a
c = b + 3
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 360 km / hr
Options: a ) 1 second , b ) 4.5 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 360 * ( 5 / 18 ) = 100 m / sec time = distance / speed = 100 / 100 = 1 second answer : a"
Answer: a
Python program:
a = 360 * const_0_2778
b = 100 / a
Problem: a 340 - liter solution of kola is made from 64 % water , 9 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 8 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 6 % . , b ) 7.5 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 26.5 % .
Rationale: "denominator : 340 + 8 + 3.2 + 6.8 = 358 numerator : 340 ( 1 - . 64 - . 09 ) + 3.2 340 ( 0.27 ) + 3.2 91.8 + 3.2 95 ratio : 95 / 358 = 0.265 answer : e"
Answer: e
Python program:
a = 64 / 100
b = 340 * a
c = 340 - b
d = 9 / 100
e = 340 * d
f = c - e
g = f + 3 
h = 340 + 3 
i = h + 8 
j = i + 6 
k = g / j
l = k * 100
Problem: if ( 5 ^ 11 ) ( 9 ^ 6 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 11 ) ( 9 ^ 6 ) = 3 ( 15 ^ x ) = > 5 ^ 11 * 3 ^ 12 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 11 * 3 ^ 12 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 11 answer c"
Answer: c
Python program:
a = 5 ** 11
b = 9 ** 6
c = a * b
d = c / 3
e = math.log(d)
f = math.log(15)
g = e / f
Problem: find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5
Options: a ) 26 , b ) 32 , c ) 25 , d ) 27 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 5 = 2 ^ 22 x 7 ^ 5 x 11 ^ 5 total number of prime factors = ( 22 + 5 + 5 ) = 32 . answer is b ."
Answer: b
Python program:
a = 5 * 11
b = a + 5 
c = b + 5
Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 5 inches wide on each side , the total area would have been ( m + 180 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 21 , b ) 36 , c ) 38 , d ) 40 , e ) 42
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 2 ) ( b + 2 ) = m - - - - ( 2 ) and ( l + 10 ) ( b + 10 ) = m + 180 - - - - - - - - - > ( l + 10 ) ( b + 10 ) - 180 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 10 ) ( b + 10 ) - 180 lb + 2 l + 2 b + 4 = lb + 10 l + 10 b + 100 - 180 simplify 8 l + 8 b = 84 - - - - - - > 2 ( l + b ) = 21 ( check eq ( 1 ) ) answer is a"
Answer: a
Python program:
a = 5 * 2
b = a ** 2
c = 1 * 2
d = c ** 2
e = b - d
f = 180 - e
g = f / 2