euclaise/mathqa_programs huggingface dataset:
Problem: there are 720 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 120 , d ) 175 , e ) 225
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 720 . hence , we have m + f = 720 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 720 / 3 = 240 solving the three equations yields the solution f = 240 , m = 480 , and d = 240 . the number of female democratic participants equals half the female participants equals 240 / 2 = 120 . answer : c"
Answer: c
Python program:
a = 720 / 3
b = a * 4
c = b - 720
d = c / 2
Problem: in the first 20 overs of a cricket game , the run rate was only 4.2 . what should be the rate in the remaining 30 overs to reach the target of 250 runs ?
Options: a ) 6.25 , b ) 6.28 , c ) 6.11 , d ) 5.53 , e ) 6.21
Rationale: "required run rate = [ 250 - ( 4.2 * 20 ) ] / 30 = 166 / 30 = 5.53 answer : d"
Answer: d
Python program:
a = 20 * 4
b = 250 - a
c = b / 30
Problem: in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 45000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 60 , e ) 80
Rationale: "0.036 * 10 ^ 5 can be written as 3600 45000 * 10 ^ ( - 3 ) can be written as 45 required = 3600 / 45 = 80 answer : e"
Answer: e
Python program:
a = 1000 * 100
b = a * 0
c = 45000 / 1000
d = b / c
Problem: if the wheel is 10 cm then the number of revolutions to cover a distance of 1200 cm is ?
Options: a ) 11 , b ) 14 , c ) 18 , d ) 19 , e ) 10
Rationale: "2 * 22 / 7 * 10 * x = 1200 = > x = 19 answer : d"
Answer: d
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 10
h = 1200 / g
Problem: in an apartment building that has 441 units , 4 out of every 7 units are currently rented , including 1 / 5 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ?
Options: a ) 45 , b ) 70 , c ) 100 , d ) 105 , e ) 140
Rationale: "rented = 4 / 7 * 441 = 252 . rented two - bedroom = 6 / 7 * 252 = 216 ; rented one - bedroom = 1 / 7 * 252 = 36 or 252 - 216 = 36 ) . rented one - bedroom units are 1 / 5 of all one - bedroom : 1 / 5 * { all one bedroom } = 36 - - > { all one - bedroom } = 180 . { all two - bedroom } = 441 - 180 = 261 . two - bedroom not rented = 261 - 216 = 45 . answer : a ."
Answer: a
Python program:
a = 441 / 7
b = 4 * a
c = 441 / 7
d = 4 * c
e = 5 + 1 
f = d / e
g = 5 * f
h = b - g
i = 1 / 5
j = h / i
k = 441 - j
l = 441 / 7
m = 4 * l
n = 5 + 1 
o = m / n
p = 5 * o
q = k - p
Problem: john was 35 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty ' s age is now 7 / 8 of john ' s . how old is betty ?
Options: a ) 24 , b ) 35 , c ) 28 , d ) 30 , e ) 32
Rationale: "assume betty ' s age on marriage = x years . john ' s age on marriage = 35 john ' s age after 5 years = 40 years . betty ' s age after 5 years = x + 5 given : x + 5 = 7 / 8 ( 40 ) = 35 therefore betty ' s current age = 35 option b"
Answer: b
Python program:
a = 7 / 8
b = 35 + 4 
c = a * b
Problem: the owner of a furniture shop charges his customer 25 % more than the cost price . if a customer paid rs . 4800 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 3840 , b ) rs . 5270 , c ) rs . 6275 , d ) rs . 6720 , e ) none of these
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 4800 ( 100 / 125 ) = rs . 3840 . answer : a"
Answer: a
Python program:
a = 25 / 100
b = 1 + a 
c = 4800 / b
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 675 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 15 , e ) 14
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 675 3 b 2 = 675 b 2 = 225 b = 15 m . answer : option d"
Answer: d
Python program:
a = 675 / 3
b = math.sqrt(a)
Problem: in a sports club with 30 members , 16 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 16 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 16 - x ) + ( 19 - x ) + x + 2 = 30 37 - 2 x + x = 30 37 - x = 30 x = 7 so 7 members play both badminton and tennis . a"
Answer: a
Python program:
a = 16 + 19 
b = a + 2 
c = b - 30
Problem: two trains 50 m and 120 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 14.8 sec , c ) 6.12 sec , d ) 10.8 sec , e ) 20.8 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 50 + 120 = 170 m . required time = 170 * 9 / 250 = 6.12 = 6.12 sec . answer : c"
Answer: c
Python program:
a = 50 + 120 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: a large field of 500 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ?
Options: a ) 205 , b ) 215 , c ) 225 , d ) 260 , e ) 270
Rationale: "average of the two areas = 500 / 2 = 250 one - fifth of the average of the two areas = 250 / 5 = 50 ⇒ difference of the two areas = 50 let area of the smaller part = x hectares . then , area of the larger part = x + 50 hectares . = > x + x + 50 = 500 = > 2 x = 450 = > x = 225 answer : c"
Answer: c
Python program:
a = 500 / 2
b = 1 + 4 
c = 1 / b
d = a * c
e = 500 - d
f = e / 2
Problem: a small college reduced its faculty by approximately 25 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 260 , c ) 224 , d ) 254 , e ) 302
Rationale: "if x is the original number of faculty members , then after 25 % reduction in faculty members number is . 75 x but we are given . 75 x = 195 x = 260 so the original number of faculty members is 260 correct answer - b"
Answer: b
Python program:
a = 100 - 25
b = a / 100
c = 195 / b
Problem: a rectangular grass field is 75 m * 55 m , it has a path of 3.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1350 , b ) s . 1327 , c ) s . 1328 , d ) s . 1397 , e ) s . 1918
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 3.5 * 2 ) 2 * 3.5 = > 959 959 * 2 = rs . 1918 answer : e"
Answer: e
Python program:
a = 3 * 5
b = 75 + a 
c = 3 * 5
d = 55 + c 
e = rectangle_area - (
f = e * rectangle_area
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 150 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 28 sec , b ) 16 sec , c ) 39 sec , d ) 18 sec , e ) 17 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 150 = 390 m . time taken = 390 / 10 = 39 sec . answer : c"
Answer: c
Python program:
a = 240 + 150 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: a bag making machine can make 20 bags per hour . if the company adjusts the machine to produce twice the amount per hour to satisfy expected rise in demand . how many bags can the machine make in the next 5 days if it works 10 hours a day ?
Options: a ) 2,000 , b ) 1,000 , c ) 400 , d ) 50 , e ) 1,500
Rationale: 20 * 2 = 40 bags per hour . 5 days * 10 hours * 40 bags per hour = 2,000 bags . answer is option a .
Answer: a
Python program:
a = 20 / 10
Problem: 0 - - - : - | - - - : - - | - : - - : - | - - : - - - | - : - - - - 1 on the number line above , the segment from 0 to 1 has been divided into fifths , as indicated by the large tick marks , and also into sevenths , as indicated by the small tick marks . what is the least possible distance z between any two of the tick marks ?
Options: a ) 1 / 70 , b ) 1 / 35 , c ) 2 / 35 , d ) 1 / 12 , e ) 1 / 7
Rationale: divisions are 0 1 / 7 2 / 7 3 / 7 4 / 7 5 / 7 6 / 7 1 1 / 5 2 / 5 3 / 5 4 / 5 5 / 5 expressing the same in terms of the lcm of 57 , i . e 35 0 7 / 35 14 / 35 21 / 35 28 / 35 35 / 35 5 / 35 10 / 35 15 / 35 20 / 35 25 / 35 30 / 35 by comparing the divisions with each other we can see 1 / 35 is the shortest possible distance between any two selected divisions . z = 1 / 35 answer is b .
Answer: b
Python program:
a = 4 + 1 
b = 3 * 10
c = a + b 
d = 1 / c
Problem: an alloy of copper and zinc contains copper and zinc in the ratio 3 : 5 . another alloy of copper and zinc contains copper and zinc in the ratio 6 : 2 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
Options: a ) 1 : 2 , b ) 2 : 2 , c ) 2 : 5 , d ) 2 : 6 , e ) 2 : 7
Rationale: "let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 3 x / 8 , and fraction of zinc in alloy _ 1 = 5 x / 8 . similarly , fraction of copper in alloy _ 2 = 6 y / 8 , and fraction of zinc in alloy _ 2 = 2 y / 8 . mixing them , we get copper = 3 x / 8 + 6 y / 8 ; zinc = 5 x / 8 + 2 y / 8 . so , 3 x + 6 y = 5 x + 2 y - > 2 x = 4 y - > x / y = 2 / 4 = 1 / 2 so , they must be mixed in the ratio 1 : 2 answer : a"
Answer: a
Python program:
a = 6 + 2 
b = 3 / a
c = 6 / 2
d = b - c
e = 6 / 2
f = 6 + 2 
g = 6 / f
h = e - g
i = d / h
Problem: david obtained 76 , 65 , 82 , 67 and 85 marks ( out in 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) 79
Rationale: "add all those marks and divide it by 5 becz they gave us 5 subjects for finding average marks we need to divide them add them 76 + 65 + 82 + 67 + 85 / 5 = 375 / 5 = 75 answer : d"
Answer: d
Python program:
a = 76 + 65 
b = a + 82 
c = b + 67 
d = c + 85 
e = 2 + 3 
f = d / e
Problem: 51 + 52 + 53 + . . . . . . . . . + 100 ) is equal to
Options: a ) 3775 , b ) 3779 , c ) 3629 , d ) 3729 , e ) 3719
Rationale: "51 + 52 + 53 + . . . . . . . . . . . + 100 = ( 1 + 2 + 3 + . . . . + 100 ) - ( ! + 2 + 3 + . . . . . . + 50 ) = = ( 5050 - 1275 ) = 3775 answer ; a"
Answer: a
Python program:
a = 100 + 51 
b = 100 * a
c = b / 52
Problem: joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 2952400 , how many months will it take joan to pay back her mortgage ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 13
Rationale: "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 2952400 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 29524 so we have 1 , 3 , 9 , 27 . . . . . 2652400 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 29524 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 29524 x - 2 = 1 - 3 ^ n - 59048 = 1 - 3 ^ n - 59049 = - 3 ^ n 59049 = 3 ^ n ( negatives cancel out ) 59049 can also be re written as 3 ^ 10 therefore ; 3 ^ 10 = 3 ^ n thus n = 10 ( c )"
Answer: c
Python program:
a = 2952400 * 2
b = a / 100
c = b + 1 
d = math.log(c)
e = math.log(3)
f = d / e
Problem: a company decreased the price of its main product by 20 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?
Options: a ) 3.0 , b ) 7.0 , c ) 5.0 , d ) 2.0 , e ) 1.0
Rationale: "for the total revenue to remain the same when the price is one fifth , the number of products sold must five times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 20 % = 5.0 answer : c"
Answer: c
Python program:
a = 100 / 20
Problem: in how many ways 4 boys and 4 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 1152 , b ) 1987 , c ) 2012 , d ) 1856 , e ) 2546
Rationale: "number of ways = 2 * 4 ! * 4 ! = 1152 answer is a"
Answer: a
Python program:
a = math.factorial(4)
b = math.factorial(4)
c = a * b
Problem: the average of first five multiples of 3 is :
Options: a ) 3 , b ) 9 , c ) 12 , d ) 15 , e ) 17
Rationale: "solution average = 3 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 45 / 5 = 9 answer b"
Answer: b
Python program:
a = 3 + 1
Problem: the average age of an adult class is 40 years . 17 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "let original strength = y then , 40 y + 17 x 32 = ( y + 17 ) x 36 â ‡ ’ 40 y + 544 = 36 y + 612 â ‡ ’ 4 y = 68 â ˆ ´ y = 17 d"
Answer: d
Python program:
a = 40 - 4
b = 17 * a
c = 17 * 32
d = b - c
e = d / 4
Problem: a train requires 12 seconds to pass a pole while it requires 27 seconds to cross a stationary train which is 300 mtrs long . find the speed of the train .
Options: a ) 60 kmph , b ) 75 kmph , c ) 80 kmph , d ) 85 kmph , e ) 72 kmph
Rationale: "in 12 s the train crosses the pole and in 27 sec the train crosses one more stationary train in 15 sec the train travels a distance of 300 mtrs speed = 300 / 15 = 20 m / s = 20 ( 3600 / 1000 ) = 20 * 18 / 5 = 72 kmph answer : e"
Answer: e
Python program:
a = 27 - 12
b = 300 / a
c = b * const_3_6
Problem: a salesman sold twice as much pears in the afternoon than in the morning . if he sold 360 kilograms of pears that day , how many kilograms did he sell in the morning and how many in the afternoon ?
Options: a ) 560 , b ) 240 , c ) 329 , d ) 443 , e ) 544
Rationale: "let x be the number of kilograms he sold in the morning . then in the afternoon he sold 2 xkilograms . so , the total is x + 2 x = 3 x this must be equal to 360 . 3 x = 360 x = 360 / 3 x = 120 therefore , the salesman sold 120 kg in the morning and 2 ⋅ 120 = 240 kg in the afternoon ."
Answer: b
Python program:
a = 360 / 3
b = a * 2
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 30 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 ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) 62 sec
Rationale: "relative speed = 30 + 30 = 60 km / hr . 60 * 5 / 18 = 50 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 50 = 60 sec . answer : d"
Answer: d
Python program:
a = 30 + 30
Problem: a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number f of people surveyed by the company ?
Options: a ) 46 , b ) 80 , c ) f = 90 , d ) f = 100 , e ) 200
Rationale: "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."
Answer: d
Python program:
a = 100 - 23
b = a + 23 
c = b + 20 
d = c / 2
e = d - 20
f = 100 - 23
g = f + 23 
h = g + 20 
i = h / 2
j = e + i
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 130 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 260 , e ) 250
Rationale: "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 130 total = 130 + 130 = 260 answer ( d )"
Answer: d
Python program:
a = 60 / 100
b = 130 * a
c = 55 / 100
d = 130 * c
e = b - d
f = 55 / 100
g = 50 / 100
h = f - g
i = e / h
Problem: two tains of equal lengths take 10 seconds and 16 seconds respectively to cross a telegraph post . if the length of each train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 12.3 , e ) 18
Rationale: "sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 16 ] m / sec = 7.5 m / sec . relative speed = ( 12 + 7.5 ) = m / sec = 19.5 m / sec . ∴ required time = ( 120 + 120 ) / 19.5 secc = 12.3 sec . answer d"
Answer: d
Python program:
a = 120 + 120 
b = 120 / 16
c = 120 / 10
d = b + c 
e = a / d
Problem: how many paying stones , each measuring 2 m * 1 m are required to pave a rectangular court yard 30 m long and 16 m board ?
Options: a ) 240
b ) 18
c ) 26
d ) 17
e ) 12
Rationale: 30 * 16 = 2 * 1 * x = > x = 240 answer : a
Answer: a
Python program:
a = rectangle_area / (
Problem: the circumferences of two circles are 268 meters and 380 meters . find the difference between the areas of the larger and the smaller circles .
Options: a ) 388.15 , b ) 2992 , c ) 4312.5 , d ) 2887.27 , e ) 5773.09
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 268 and 2 ∏ l = 380 s = 268 / 2 ∏ and l = 380 / 2 ∏ difference between the areas = ∏ l 2 - ∏ s 2 = ∏ { 1902 / ∏ 2 - 1342 / ∏ 2 } = 1902 / ∏ - 1342 / ∏ = ( 190 - 134 ) ( 190 + 134 ) / ∏ = ( 56 ) ( 324 ) / ( 22 / 7 ) = ( 18144 ) / ( 22 ) ( 7 ) = 5773.09 sq m . answer : e"
Answer: e
Python program:
a = 2 * math.pi
b = 380 / a
c = circle_area - (
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind roe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 15 miles ahead of roe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . roe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 15 miles . teena can cover 7.5 miles in 30 mins teena will cover 15 miles in 60 mins so answer 30 + 60 = 90 mins . d"
Answer: d
Python program:
a = 55 - 40
b = a + 7 
c = 55 - 40
d = b / c
e = d * const_60
Problem: the difference between the local value and the face value of 3 in the numeral 62975143 is
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 5
Rationale: "explanation : ( local value of 3 ) - ( face value of 3 ) = ( 3 - 3 ) = 0 d )"
Answer: d
Python program:
a = 3 * 1000
b = a - 3
Problem: the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 36 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: first , let ' s translate the expression 21 # 36 , using the definition given : 21 # 36 = 21 × 24 × 27 × 30 × 33 × 36 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 36 = 3 ^ 6 ( 7 × 8 × 9 × 10 × 11 × 12 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 36 = 3 ^ 6 ( 7 × 2 ^ 3 × 3 ^ 2 × ( 2 × 5 ) × 11 × ( 2 ^ 2 × 3 ) ) let ' s group the prime bases : 21 # 36 = 2 ^ 6 × 3 ^ 9 × 5 × 7 × 11 the sum of the exponents is 6 + 9 + 1 + 1 + 1 = 18 the answer is c .
Answer: c
Python program:
a = 2 + 2 
b = 3 + a 
c = 2 + 2 
d = b + c 
e = 2 + 2 
f = 3 + e 
g = d + f
Problem: a grocer has a sale of rs . 435 , rs . 927 , rs . 855 , rs . 230 and rs . 562 for 5 consecutive days . how much sale must he have in the sixth day so that he gets an average sale of rs . 625 ?
Options: a ) rs 741 , b ) rs 5991 , c ) rs 6001 , d ) rs 6991 , e ) none of these
Rationale: "explanation : total sale for 5 days = rs . ( 435 + 927 + 855 + 230 + 562 ) = rs . 3009 . required sale = rs . [ ( 625 x 6 ) - 3009 ] = rs . ( 3750 - 3009 ) = rs . 741 . answer : a"
Answer: a
Python program:
a = 5 + 1 
b = a * 625
c = 435 + 927 
d = c + 855 
e = d + 230 
f = e + 562 
g = b - f
Problem: the monthly rent of a shop of dimension 10 feet × 8 feet is rs . 2400 . what is the annual rent per square foot of the shop ?
Options: a ) 43 , b ) 56 , c ) 68 , d ) 360 , e ) 92
Rationale: "sol . monthly rent per square feet = 2400 / ( 10 * 8 ) = 30 & annual rent per square feet = 12 * 30 = 360 answer : d"
Answer: d
Python program:
a = 10 + 2 
b = 2400 / rectangle_area
c = a * b
Problem: find compound interest on $ 12000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 4663.5 , b ) 4203.5 , c ) 4303.5 , d ) 4403.5 , e ) 4103.5
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 12000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 12000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 16663.50 . : . c . i . = rs . ( 16663.50 - 12000 ) = $ 4663.50 answer a ."
Answer: a
Python program:
a = 15 / 100
b = 12000 * a
c = 15 / 100
d = 12000 * c
e = 12000 + d 
f = 15 / 100
g = e * f
h = b + g 
i = 15 / 100
j = 12000 * i
k = 12000 + j 
l = 15 / 100
m = 12000 * l
n = 12000 + m 
o = 15 / 100
p = n * o
q = k + p 
r = 15 / 100
s = r / 3
t = q * s
u = h + t
Problem: after decreasing 24 % in the price of an article costs rs . 320 . find the actual cost of an article ?
Options: a ) 400 , b ) 520 , c ) 651 , d ) 525 , e ) 421
Rationale: "cp * ( 76 / 100 ) = 320 cp = 4.21 * 100 = > cp = 421 answer : e"
Answer: e
Python program:
a = 24 / 100
b = 1 - a
c = 320 / b
Problem: in a group of 800 people , 1 / 5 play at least one instrument , 32 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 2 / 125 , b ) 4 / 25 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5
Rationale: "p ( playing 2 or more instruments ) = 32 / 800 = 1 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 1 / 25 = 4 / 25 . answer b ."
Answer: b
Python program:
a = 800 * 1
b = a / 5
c = b - 32
d = c / 800
Problem: teacher took exam for english , average for the entire class was 80 marks . if we say that 10 % of the students scored 95 marks and 20 % scored 90 marks then calcualte average marks of the remaining students of the class .
Options: a ) 60 , b ) 70 , c ) 65 , d ) 75 , e ) 80
Rationale: lets assume that total number of students in class is 100 and required average be x . then from the given statement we can calculate : ( 10 * 95 ) + ( 20 * 90 ) + ( 70 * x ) = ( 100 * 80 ) 70 x = 8000 - ( 950 + 1800 ) = 5250 answer : d x = 75 .
Answer: d
Python program:
a = 10 / 100
b = a * 95
c = 80 - b
d = 20 / 100
e = d * 90
f = c - e
g = 10 / 100
h = 20 / 100
i = g + h 
j = 1 - i
k = f / j