euclaise/mathqa_programs huggingface dataset:
Problem: the average age of 30 students of a class is 20 years . out of these , the average age of 10 students is 16 years and that of the other 19 students is 22 years . the age of the 30 th student is :
Options: a ) 22 years , b ) 24 years , c ) 15 years , d ) 16 years , e ) none of these
Rationale: "explanation : age of the 30 th student = [ 30 x 20 - ( 10 x 16 + 19 x 22 ) ] = ( 600 - 278 ) = 22 years . answer : a"
Answer: a
Python program:
a = 30 * 30
b = 10 * 16
c = 19 * 22
d = b + c 
e = a - d
Problem: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 4 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 28 km , b ) 20 km , c ) 65 km , d ) 18 km , e ) 16 km
Rationale: "distance = relative speed * time = ( 4 + 3 ) * 4 = 28 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : a"
Answer: a
Python program:
a = 4 + 3 
b = a * 4
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 176 votes . find the total number of valid votes ?
Options: a ) 440 , b ) 570 , c ) 480 , d ) 520 , e ) 550
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 176 = > 4 x / 10 = 176 = > 4 x = 1760 = > x = 440 . answer : a"
Answer: a
Python program:
a = 100 - 70
b = 70 - a
c = b / 100
d = 176 / c
Problem: ( 17 ) 5.25 x ( 17 ) ? = 178
Options: a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 4.5 , e ) none of these
Rationale: "solution let ( 17 ) 5.25 * ( 17 ) x = 178 . then , ( 17 ) 5.25 + x = ( 17 ) 8 . ∴ 5.25 + x = 8 ⇔ x = ( 8 - 5.25 ) ⇔ x = 2.75 answer b"
Answer: b
Python program:
a = 17 * 17
Problem: in measuring the sides of a rectangle , one side is taken 20 % in excess and the other 10 % in deficit . find the error per cent in area calculated from the measurement ?
Options: a ) 12 % deficit
b ) 10 % excess
c ) 8 % excess
d ) 9 % excess
e ) none of these
Rationale: since side 1 x side 2 = area therefore , error % in area = ( x + y + xy / 100 ) % = [ 20 - 10 + ( - 10 x 20 ) / 100 ] % or 8 % i . e . , 8 % excess answer : c
Answer: c
Python program:
a = 20 - 10
b = 20 * 10
c = b / 100
d = a - c
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 54 kmph , find the speed of the stream ?
Options: a ) 77 , b ) 18 , c ) 14 , d ) 12 , e ) 17
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 54 / 3 = 18 kmph . answer : b"
Answer: b
Python program:
a = 54 * 2
b = a / 3
c = 54 - b
Problem: some ladies can do a piece of work in 12 days . two times the number of such ladies will do half of that work in :
Options: a ) 6 days , b ) 4 days , c ) 12 days , d ) 3 days , e ) 8 days
Rationale: expl : let x ladies can do the work in 12 days . more ladies , less days ( indirect ) less work , less days ( direct ) ladies 2 x : x work 1 : ½ 2 x : x , 1 : ½ : : 12 : y : . 2 x * 1 * y = x * ½ * 12 or y = 3 hence the required number of days = 3 answer : d
Answer: d
Python program:
a = 12 / 4
Problem: think of a number , divide it by 5 and add 6 to it . the result is 65 . what is the number thought of ?
Options: a ) 24 , b ) 77 , c ) 295 , d ) 267 , e ) 29
Rationale: "explanation : 65 - 6 = 59 59 x 5 = 295 answer : c"
Answer: c
Python program:
a = 65 - 6
b = a * 5
Problem: sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 200 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 4 of the days were hot , then what was the price of 1 cup on a hot day ?
Options: a ) $ 1.56 , b ) $ 1.88 , c ) $ 2.25 , d ) $ 2.50 , e ) $ 3.25
Rationale: "6 regular days - - > sales = 6 * 32 * x = 192 x ; 4 hot days - - > sales = 4 * 32 * ( 1.25 x ) = 160 x ; total sales = 192 x + 160 x = 352 x . total cost = 10 * 32 * 0.75 = 240 . profit = 352 x - 240 = 200 - - > x = 1.25 . 1.25 x = ~ 1.56 . answer : a ."
Answer: a
Python program:
a = 75 / 100
b = 32 * a
c = 4 + 1 
d = c * 2
e = b * d
f = e + 200 
g = 4 + 1 
h = g * 2
i = h - 4
j = i * 32
k = 100 + 25 
l = k / 100
m = l * 4
n = m * 32
o = j + n 
p = f / o
q = 100 + 25 
r = q / 100
s = p * r
Problem: a candidate got 32 % of the votes polled and he lost to his rival by 1908 votes . how many votes were cast ?
Options: a ) 5100 , b ) 5200 , c ) 5300 , d ) 5400 , e ) 5500
Rationale: "let x be the total number of votes . 0.32 x + 1908 = 0.68 x 0.36 x = 1908 x = 1908 / 0.36 = 5300 the answer is c ."
Answer: c
Python program:
a = 32 / 100
b = 1 - a
c = 32 / 100
d = b - c
e = 1908 / d
Problem: the sub - duplicate ratio of 1 : 9 is
Options: a ) 4 : 3 , b ) 1 : 2 , c ) 1 : 3 , d ) 1 : 4 , e ) 2 : 3
Rationale: "root ( 1 ) : root ( 9 ) = 1 : 3 answer : c"
Answer: c
Python program:
a = math.sqrt(1)
b = math.sqrt(9)
c = a / b
Problem: a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 482 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 3377 , b ) 6886 , c ) 2788 , d ) 2000 , e ) 28712
Rationale: "p ( 11 / 10 ) 4 - p ( 6 / 5 ) 2 = 482 p = 2000 answer : d"
Answer: d
Python program:
a = 20 + 1 
b = 20 + 1 
c = a * b
d = 20 + 1 
e = c + d
Problem: what is the value of 10 ^ 8 - 6 ^ 4 ?
Options: a ) 9,99 , 98,623 , b ) 9,99 , 98,704 , c ) 9,99 , 98,800 , d ) 9,99 , 99,521 , e ) 9,99 , 99,932
Rationale: "as 10 ^ n will always have last digit as 0 and 6 ^ n will always as last digit 6 . . hence difference of such sum should always be ending with 4 and there is only on option . . answer b"
Answer: b
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 10
d = c / 100
Problem: what is the area of a square field whose diagonal of length 14 m ?
Options: a ) 160 sq m , b ) 140 sq m , c ) 200 sq m , d ) 400 sq m , e ) 180 sq m
Rationale: "d 2 / 2 = ( 14 * 14 ) / 2 = 140 answer : b"
Answer: b
Python program:
a = square_area / (
Problem: harish can paint a wall in just 3 hours . however it takes 6 hours for ganpat to complete the same job of painting the wall . how long would it take for both of them to paint the wall , if both work together ?
Options: a ) 3 hours , b ) 1 hours , c ) 3.20 hours , d ) 2 hours , e ) 1.35 hours
Rationale: d two hours . harish who could paint the wall in 3 hours could paint 2 / 3 of the wall in just two hours . ganpat who paint the wall in 6 hours could paint 1 / 3 of the wall in two hours . 2 / 3 + 1 / 3 = 1 .
Answer: d
Python program:
a = 1/(3)
b = 1/(6)
c = a + b 
d = 1/(c)
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 38 years . what is deepak present age ?
Options: a ) 22 , b ) 24 , c ) 77 , d ) 266 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 38 = > x = 8 so deepak age is = 3 ( 8 ) = 24 answer : b"
Answer: b
Python program:
a = 38 - 6
b = a * 3
c = b / 4
Problem: two pipes a and b can fill a tank in 40 and 120 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 30 , b ) 35 , c ) 25 , d ) 82 , e ) 22
Rationale: "part filled by a in 1 min . = 1 / 40 part filled by b in 1 min . = 1 / 120 part filled by ( a + b ) in 1 min . = 1 / 40 + 1 / 120 = 1 / 30 . both the pipes can fill the tank in 30 minutes . answer : a"
Answer: a
Python program:
a = 40 * 100
b = 1 / 40
c = 1 / 120
d = b + c 
e = d * 2
f = 1 - e
g = f * 40
h = g * const_60
i = a + h
Problem: rs 70000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 8000 find money given by 10 % ?
Options: a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000
Rationale: "let first parrt is x and second part is y then x + y = 70000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 8000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 80000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 80000 = 70000 + y so y = 10000 then x = 70000 - 10000 = 60000 first part = 60000 answer : d"
Answer: d
Python program:
a = 70000 * 20
b = a / 100
c = b - 8000
d = 10 / 100
e = c / d
Problem: in a two digit number , the digit in the units place is 6 times the digit in 10 ' s place and sum of the digits is equal to 7 . what is the number ?
Options: a ) 16 , b ) 28 , c ) 32 , d ) 36 , e ) 38
Rationale: solution let the ten digits be x . then , units digit = 6 x therefore x + 6 x = 7 ‹ = › 7 x = 7 ‹ = › x = 1 . so , ten ' s digit = 1 , unit ' s digit = 6 . hence , the required number is 16 . answer a
Answer: a
Python program:
a = 6 + 1 
b = 7 / a
c = b * 10
d = 6 + 1 
e = 7 / d
f = 6 * e
g = c + f
Problem: shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 40 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 40 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 38 , d ) 40 , e ) 46
Rationale: "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 38 hence answer is c"
Answer: c
Python program:
a = 3 * 40
b = a - 40
c = b / 3
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2340 , what will be b ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 520 , c ) $ 780 , d ) $ 1170 , e ) $ 630
Rationale: explanatory answer a , b and c will share the amount of $ 2340 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 2340 will be 4 : 3 : 2 . hence , b ' s share will be 3 * 2340 / 9 = 780 correct choice is ( c )
Answer: c
Python program:
a = 1/(8)
b = 1/(12)
c = 1/(6)
d = 1/(8)
e = c + d 
f = b + e 
g = a / f
h = 2340 * g
Problem: in an exam , amar scored 64 percent , bhavan scored 36 percent and chetan 44 percent . the maximum score awarded in the exam is 900 . find the average mark scored by all the 3 boys ?
Options: a ) 384 , b ) 432 , c ) 207 , d ) 269 , e ) 208
Rationale: average mark scored by all the three boys = [ 64 / 100 ( 900 ) + 36 / 100 ( 900 ) + 44 / 100 ( 900 ) ] / 3 = 432 answer : b
Answer: b
Python program:
a = 44 / 100
b = a * 900
c = 64 / 100
d = c * 900
e = 36 / 100
f = e * 900
g = d + f 
h = b + g 
i = h / 3
Problem: a 280 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 330 m
Rationale: "relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 280 ) / 9 = 500 / 9 x + 280 = 500 x = 220 . a"
Answer: a
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 280
Problem: find the average of first 5 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 21
Rationale: "average = ( 5 + 10 + 15 + 20 + 25 ) / 5 = 15 answer is b"
Answer: b
Python program:
a = 5 + 1 
b = 5 + 1 
c = b + 2 
d = a + c 
e = 5 - 5
f = 5 - 2
g = e + f 
h = d + g 
i = h / 5
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 108 km / hr . what is the length of the platform ?
Options: a ) 229 , b ) 240 , c ) 288 , d ) 480 , e ) 221
Rationale: "speed = 108 * 5 / 18 = 30 m / sec . length of the train = 30 * 20 = 600 m . let the length of the platform be x m . then , ( x + 600 ) / 36 = 30 = > x = 480 m . answer : d"
Answer: d
Python program:
a = 108 * const_0_2778
b = 20 * a
Problem: a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 2.9 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
Options: a ) 1.6 , b ) 1.9 , c ) 2.2 , d ) 2.5 , e ) 2.8
Rationale: "72 km / hr = 1.2 km / min the total distance is 3 km . 3 / 1.2 = 2.5 minutes the answer is d ."
Answer: d
Python program:
a = 100 / 1000
b = 2 + 9 
c = b / 72
d = c * const_60
Problem: a train 120 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 7.2 sec , b ) 9.3 sec , c ) 12 sec , d ) 15.2 sec , e ) 18 sec
Rationale: speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 120 m at 50 / 3 m / sec = 120 * 3 / 50 sec = 7.2 sec answer : a .
Answer: a
Python program:
a = 68 - 8
b = a * const_0_2778
c = 120 / b
Problem: if exactly 7 guests drank only one of the two types of drinks , how many guests drank both types of drinks ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 4 , e ) 2
Rationale: say x guests drank both drinks . ( 7 - x ) + ( 4 - x ) = 7 - - > x = 2 . answer : e .
Answer: e
Python program:
a = 7 * 2
Problem: a triangle has sides 10 , 17 , and 21 . a square is inscribed in the triangle . one side of the square lies on the longest side of the triangle . the other two vertices of the square touch the two shorter sides of the triangle . what is the length of the side of the square ?
Options: a ) 148 / 29
b ) 168 / 29
c ) 168 / 26
d ) 158 / 29
e ) 198 / 29
Rationale: by heron ' s formula , the area , a , of a triangle with sides a , b , c is given by a = square root [ s ( s − a ) ( s − b ) ( s − c ) ] , where s = ½ ( a + b + c ) is the semi - perimeter of the triangle . then s = ½ ( 10 + 17 + 21 ) = 24 , and a = 84 . a square inscribed in a 10 by 17 by 21 triangle , with perpendicular dropped onto the side of length 21 . now drop a perpendicular of length h onto the side of length 21 . we also have a = ½ × base × perpendicular height . hence a = 21 h / 2 = 84 , from which h = 8 . notice that the triangle above the square is similar to the whole triangle . ( this follows because its base , the top of the square , is parallel to the base of the whole triangle . ) let the square have side of length d . considering the ratio of altitude to base in each triangle , we have 8 / 21 = ( 8 − d ) / d = 8 / d − 1 . therefore the length of the side of the square is 168 / 29 . answer : b
Answer: b
Python program:
a = triangle_area_three_edges * (
b = a / 2
c = b / 21
Problem: if a train , travelling at a speed of 160 kmph , crosses a pole in 9 sec , then the length of train is ?
Options: a ) 281 , b ) 125 , c ) 288 , d ) 266 , e ) 400
Rationale: "d = 160 * 5 / 18 * 9 = 400 m answer : e"
Answer: e
Python program:
a = 160 * const_0_2778
b = a * 9
Problem: due to construction , the speed limit along an 15 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 5 , b ) 8 , c ) 9.36 , d ) 15 , e ) 24
Rationale: "old time in minutes to cross 15 miles stretch = 15 * 60 / 55 = 15 * 12 / 11 = 16.36 new time in minutes to cross 15 miles stretch = 15 * 60 / 35 = 15 * 12 / 7 = 25.71 time difference = 9.36 answer c )"
Answer: c
Python program:
a = 55 + 15 
b = a - 1
c = 15 / 35
d = 15 / 55
e = c - d
f = b * e
g = max(f)
Problem: [ ( 3.242 x 12 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) 0.038904
Rationale: answer multiplying 3.242 x 12 = 3.8904 now divide 3.8904 by 100 so , 3.8904 ÷ 100 = 0.038904 ∴ shift the decimal two places to the left as 100 correct option : e
Answer: e
Python program:
a = 3 * 242
b = a / 100
c = b / 10
Problem: for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 5 ] * [ 6 ] equivalent to ?
Options: a ) [ 45 ] , b ) [ 30 ] , c ) [ 15 ] , d ) [ 5 ] , e ) [ 50 ]
Rationale: "[ 5 ] * [ 6 ] = 15 * 3 = 45 = [ 15 ] the answer is c ."
Answer: c
Python program:
a = 6 / 2
b = 3 * 5
c = a * b
d = c / 3
Problem: find the c . i . on a sum of rs . 10000 for 9 months at 20 % per annum , interest being compounded quarterly ?
Options: a ) 2000 , b ) 10025 , c ) 1025 , d ) 2015 , e ) 2025
Rationale: "c . i . = 10000 ( 21 / 20 ) ^ 3 - 10000 = 1025 answer : c"
Answer: c
Python program:
a = const_0_25 / 4
b = 1 + a 
c = const_0_25 / 4
d = 1 + c 
e = b * d
f = 10000 * e
g = f - 10000
Problem: a person crosses a 720 m long street in 12 minutes . what is his speed in km per hour ?
Options: a ) 3.6 , b ) 4.5 , c ) 4.8 , d ) 5.4 , e ) 5.5
Rationale: "speed = 720 / ( 12 x 60 ) m / sec = 1 m / sec . converting m / sec to km / hr = 1 x ( 18 / 5 ) km / hr = 3.6 km / hr . answer : a"
Answer: a
Python program:
a = 720 / 1000
b = 12 * const_60
c = b / 3600
d = a / c
Problem: in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 28 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 70 , b ) 245 , c ) 150 , d ) 200 , e ) 350
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 28 , so 0.14 * { total } = 28 - - > { total } = 200 . answer : d ."
Answer: d
Python program:
a = 100 - 30
b = a / 100
c = 20 / 100
d = b * c
e = 28 / d
Problem: if 22 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 125 , b ) 187 , c ) 231 , d ) 375 , e ) 460
Rationale: "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 22 lines is 22 c 2 = 231 the answer is c ."
Answer: c
Python program:
a = math.factorial(22)
b = 22 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: the population of a town increased from 1 , 75,000 to 2 , 45,000 in a decade . the average percent increase of population per year is
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none
Rationale: "solution increase in 10 years = ( 245000 - 175000 ) = 87500 . increase % = ( 70000 / 175000 ã — 100 ) % = 40 % . required average = ( 40 / 10 ) % = 4 % . answer a"
Answer: a
Python program:
a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 2 + 3 
f = e * 100
g = d - f
h = 3 + 4 
i = h * 10
j = 2 + 3 
k = i + j 
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
Problem: how many integers between 1 and 10 ^ 20 are such that the sum of their digits is 2 ?
Options: a ) 190 , b ) 210 , c ) 211 , d ) 230 , e ) 231
Rationale: "the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 19 and there are 20 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 19 thus , the total number of integers is 1 + 2 + . . . + 19 + 20 = 20 * 21 / 2 = 210 the answer is b ."
Answer: b
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 10 - e
Problem: the price of commodity x increases by 40 paise every year , while the price of commodity y increases by 15 paise every year . if in 1988 , the price of commodity x was 4.20 and that of y was 6.30 , in which year will commodity x cost 40 paise more than commodity y ?
Options: a ) 1997 , b ) 1998 , c ) 1999 , d ) 2000 , e ) none of these
Rationale: suppose in ‘ n ’ years the price of comodity x will be more by 40 paise than that of commodity y . ∴ 420 + 40 n – 630 – 15 n = 40 or , 25 n – 210 = 40 or , 25 n = 250 or , n = 250 ⁄ 25 = 10 years . answer b
Answer: b
Python program:
a = 40 / 100
b = 6 - 3
c = a + b 
d = 40 / 100
e = 15 / 100
f = d - e
g = c / f
h = 1988 + g
Problem: when tom works alone he chops 4 lb . salad in 3 minutes , and when tammy works alone she chops 3 lb . salad in 4 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tammy is what percent greater than the quantifying chopped by tom ? .
Options: a ) 125 % , b ) 100 % , c ) 25 % , d ) 225 % , e ) 400 %
Rationale: "tom chops 8 lbs in 12 minutes tammy chopswhen tom works alone he chops 2 lb . salad in 3 minutes , and when tammy works alone she chops 3 lb . salad in 2 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tammy is what percent greater than the quantifying chopped by tom ? . 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . ans : a"
Answer: a
Python program:
a = 3 / 4
b = 2 / 0
c = a - b
d = 4 / 3
e = c / d
f = e * 100
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 45 percent on clothing , 45 percent on food , and 10 percent on other items . if jill paid a 5 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 3.5 , b ) 3.35 , c ) 3.45 , d ) 3.25 , e ) 3.55
Rationale: "assume she has $ 200 to spend . tax clothing = 45 % = $ 90 = $ 4.5 food = 45 % = $ 90 = $ 0.00 items = 10 % = $ 20 = $ 2.00 total tax = $ 6.50 % of total amount = 6.5 / 200 * 100 = 3.25 % answer d"
Answer: d
Python program:
a = 5 / 100
b = 45 * a
c = 10 / 100
d = 10 * c
e = b + d 
f = e / 100
g = f * 100
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 10 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 2.9 hrs , b ) 8.9 hrs , c ) 2.9 hrs , d ) 6.7 hrs , e ) 8.6 hrs
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 10 ) = 3 / 20 the cistern will be filled in 20 / 3 hrs i . e . , 6.7 hrs . answer : d"
Answer: d
Python program:
a = 1 / 4
b = 1 / 10
c = a - b
d = 1 / c