euclaise/mathqa_programs huggingface dataset:
Problem: find the probability that a non leap year selected at random will have 53 sundays
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 7
Rationale: "there are 365 days in a leap year : 52 weeks and 1 more days . so , 52 sundays and 1 days . this 1 days can be { mon , tue , wed , thu , fri , sat , sun } ( 7 cases ) . in order to have 53 sundays we should have sun case . the probability of that is 1 / 7 . answer : e ."
Answer: e
Python program:
a = 3 + 4 
b = 2 / a
Problem: when a number is divided by 6 & then multiply by 12 the answer is 11 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6
Rationale: "if $ x $ is the number , x / 6 * 12 = 11 = > 2 x = 11 = > x = 5.5 c"
Answer: c
Python program:
a = 11 / 12
b = a * 6
Problem: if 3 x + 4 y = 60 and 6 x - 4 y = 12 , what is the product of x and y ?
Options: a ) 80 , b ) 54 , c ) 54 , d ) 72 , e ) 12
Rationale: given 3 x + 4 y = 60 - - - eq 1 6 x - 4 y = 12 - - eq 2 sum both eqns we get 9 x = 72 = > x = 8 sum 6 x in eq 2 = > 48 - 4 y = 12 . = > y = 9 now xy = 8 * 9 = 72 option d is correct answer .
Answer: d
Python program:
a = 60 + 12 
b = 6 + 3 
c = a / b
d = 60 + 12 
e = 6 + 3 
f = d / e
g = 6 * f
h = g - 12
i = h / 4
j = c * i
Problem: a rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm . how many times can it go round a cylinder having radius 20 cm ?
Options: a ) 49 rounds
b ) 42 rounds
c ) 54 rounds
d ) 52 rounds
e ) none of these
Rationale: explanation : let the required number of rounds be x more radius , less rounds ( indirect proportion ) hence we can write as radius 14 : 20 } : : x : 70 ⇒ 14 × 70 = 20 x ⇒ 14 × 7 = 2 x ⇒ x = 7 × 7 = 49 . answer : option a
Answer: a
Python program:
a = circumface * (
b = a / 70
Problem: a seller of used cars has 18 cars to sell and each of his clients selected 3 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 18 , e ) 16
Rationale: "ifno caris selected more than once then the number of clients = 18 / 3 = 6 but since every car is being selected three times so no . of clients must be thrice as well = 6 * 3 = 18 answer : option d"
Answer: d
Python program:
a = 18 / 3
b = a * 3
Problem: what percent of 120 are 90 ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 33 % , e ) 30 %
Rationale: "explanation : ( ? % / 100 ) * 120 = 90 ? = 75 % answer is c"
Answer: c
Python program:
a = 120 / 90
b = a * 100
Problem: vijay sells a cupboard at 12 % below cost price . had he got rs . 1650 more , he would have made a profit of 12 % . what is the cost price of the cupboard ?
Options: a ) 7450 , b ) 14900 , c ) 7400 , d ) 6875 , e ) none of these
Rationale: "explanation : cost price = 1650 / ( 0.12 + 0.12 ) = 2086 / 0.24 = rs . 6875 answer d"
Answer: d
Python program:
a = 100 + 12 
b = 100 - 12
c = a - b
d = c / 100
e = 1650 / d
Problem: a hostel had provisions for 250 men for 48 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 48 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 48 250 × 48 = 200 x 5 × 48 = 4 x x = 5 × 12 = 60 answer d"
Answer: d
Python program:
a = 250 * 48
b = 250 - 50
c = a / b
Problem: 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 12 such machines to perform the same job ?
Options: a ) 6 hours , b ) 8.75 hours , c ) 12 hours , d ) 4 hours , e ) 16 hours
Rationale: "let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 3 machines 12 units of work ( 12 machines ) - - - > 1 hour for 48 units of work 12 * 4 - - - > 1 * 4 hours d 4 hours"
Answer: d
Python program:
a = 6 * 8
b = a / 12
Problem: if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 70 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 1 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 130 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 70 ) = ( r + 5 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 1 ) x = 130 ans c"
Answer: c
Python program:
a = 70 - 5
b = a * 1
c = 1 * 10
d = b + c
Problem: if a 5 percent deposit that has been paid toward the purchase of a certain product is $ 50 , how much more remains to be paid ?
Options: a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950
Rationale: "95 % remains to be paid so the remaining amount is 19 * 50 = $ 950 . the answer is e ."
Answer: e
Python program:
a = 100 / 5
b = 50 * a
c = b - 50
Problem: john buys good worth rs . 6650 . he gets a rebate of 6 % on it . after getting the rebate , he pays sales tax @ 10 % . find the amount he will have to pay for the goods .
Options: a ) rs . 6876.10 , b ) rs . 4500 , c ) rs . 4600 , d ) rs . 3400 , e ) rs . 7500
Rationale: rebate = 6 % of rs . 6650 = rs . 6 x 6650 = rs . 399 . 100 sales tax = 10 % of rs . ( 6650 - 399 ) = rs . 10 x 6251 = rs . 625.10 100 final amount = rs . ( 6251 + 625.10 ) = rs . 6876.10 correct answer - a
Answer: a
Python program:
a = 10 / 100
b = 6 / 100
c = b * 6650
d = 6650 - c
e = a * d
f = 6 / 100
g = f * 6650
h = 6650 - g
i = e + h
Problem: the ratio of the adjacent angles of a parallelogram is 4 : 11 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 132 ° , b ) 228 ° , c ) 156 ° , d ) 224 ° , e ) none of these
Rationale: the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 4 x + 11 x = 180 ° or , 15 x = 180 ° or , x = 12 ° hence the angles of the parallelogram are 48 ° and 132 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 48 ° + 84 ° = 132 ° answer : a
Answer: a
Python program:
a = 4 * 2
b = a * 10
c = b + 100 
d = c * 2
e = 5 + 6 
f = e + 7 
g = f + 12 
h = d / g
i = h * 11
Problem: a and b start a business , with a investing the total capital of rs . 25000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 250 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
Options: a ) a ) 22500 , b ) b ) 33500 , c ) c ) 22510 , d ) d ) 33510 , e ) e ) 11500
Rationale: "interest received by a from b = 10 % of half of rs . 25000 = 10 % * 12500 = 1250 . amount received by a per annum for being a working partner = 250 * 12 = rs . 3000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 1250 + 3000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 1250 + 3000 + p ) = 2 ( p ) p = 4250 total profit = 2 p + 3000 = 2 * 4250 + 3000 = 11500 answer : e"
Answer: e
Python program:
a = 25000 / 2
b = a / 10
c = b * 3
d = c * 4
e = d + 250
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 38 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 229 , b ) 787 , c ) 152 , d ) 128 , e ) 121
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 38 4 / x = 1 / 38 = > x = 152 min . answer : c"
Answer: c
Python program:
a = 1 + 4 
b = a * 38
Problem: a circular dartboard of radius 1 foot is at a distance of 20 feet from you . you throw a dart at it and it hits the dartboard at some point q in the circle . what is the probability that q is closer to the center of the circle than the periphery ?
Options: a ) 0.75 , b ) 1 , c ) 0.25 , d ) 0.5 , e ) 0.58
Rationale: radius of inner dartboard / overall radius of dartboard ( ( r / 2 ) ^ 2 ) / ( r ^ 2 ) = 1 / 4 = 0.25 answer : c
Answer: c
Python program:
a = 1 / 2
b = 1 / 2
c = a * b
d = 1 * 1
e = c / d
Problem: a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 76 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 2 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 76 / 25 = 3 . . . . so the max is 3 76 / 20 = 3 . . . so the max is 3 76 - 75 = 1 answer : b"
Answer: b
Python program:
a = 25 - 20
Problem: a , b and c have rs . 700 between them , a and c together have rs . 300 and b and c rs . 600 . how much does c have ?
Options: a ) 200 , b ) 250 , c ) 300 , d ) 350 , e ) 400
Rationale: "a + b + c = 700 a + c = 300 b + c = 600 - - - - - - - - - - - - - - a + b + 2 c = 900 a + b + c = 700 - - - - - - - - - - - - - - - - c = 200 answer : a"
Answer: a
Python program:
a = 300 + 600 
b = a - 700
Problem: a and b together can do a work in 7 days . if a alone can do it in 14 days . in how many days can b alone do it ?
Options: a ) 14 , b ) 10 , c ) 21 , d ) 20 , e ) 25
Rationale: "a 14 1 / 7 â € “ 1 / 14 = 1 / 14 = > 14"
Answer: a
Python program:
a = 1 / 7
b = 1 / 14
c = a - b
d = 1/(c)
e = 2 + 3 
f = 2 / e
g = d + f
Problem: a and b start walking towards each other at 7 am at speed of 12 kmph and 13 kmph . they were initially 25 km apart . at what time do they meet ?
Options: a ) 8 pm , b ) 6 am , c ) 7 am , d ) 10 am , e ) 8 am
Rationale: "time of meeting = distance / relative speed = 25 / 13 + 12 = 25 / 25 = 1 hr after 7 pm = 8 am answer is e"
Answer: e
Python program:
a = 12 + 13 
b = 25 / a
c = 7 + b
Problem: find the lowest common multiple of 24 , 36 and 42 .
Options: a ) 360 , b ) 504 , c ) 510 , d ) 320 , e ) 280
Rationale: "lcm = 2 * 2 * 2 * 3 * 3 * 7 = 504 . answer is b"
Answer: b
Python program:
a = math.lcm(24, 36)
b = math.lcm(a, 42)
Problem: if a / b = 1 / 7 , b / c = 3 , c / d = 2 / 3 , d / e = 2 and e / f = 1 / 2 , then what is the value of abc / def ?
Options: a ) 72 / 21 , b ) 27 / 85 , c ) 34 / 47 , d ) 13 / 81 , e ) 16 / 21
Rationale: "say a = 1 . then : a / b = 1 / 7 - - > b = 7 ; b / c = 3 - - > c = 7 / 3 ; c / d = 2 / 3 - - > d = 7 / 2 ; d / e = 2 - - > e = 7 / 4 ; e / f = 1 / 2 - - > f = 7 / 2 . abc / def = ( 1 * 7 * 7 / 3 ) / ( 7 / 2 * 7 / 4 * 7 / 2 ) = 16 / 21 . answer : e ."
Answer: e
Python program:
a = 7 * 7
b = 7 * 2
c = 3 * b
d = a / c
Problem: what is the least value of x . so that 43 x 87 is divisible by 3 ?
Options: a ) 4 , b ) 5 , c ) 2 , d ) 6 , e ) 7
Rationale: "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 4 + 3 + x + 8 + 7 = 22 + x least value of x may be 2 therefore 22 + 2 = 24 is divisible by 3 . c"
Answer: c
Python program:
a = math.lcm(43, 87)
b = a / 87
c = b / 4
d = c / 4
Problem: 675.987 - ? + 56.84 = 289.654
Options: a ) a ) 443.173 , b ) b ) 752.804 , c ) c ) 714.642 , d ) d ) 629.906 , e ) of these
Rationale: "explanation : 443.173 answer : option a"
Answer: a
Python program:
a = 675 / 987
b = a * 56
c = 1 / 3
d = 675 / 987
e = d * 56
f = c * e
g = b - f
Problem: if shares of two persons in profits are rs . 800 and rs . 600 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 5
Rationale: "total profit = 1000 ratio = 800 / 600 = 4 : 3 answer : c"
Answer: c
Python program:
a = 800 / 600
Problem: if 7 / 10 of a pencil is green , 4 / 5 of the remaining is gold and the remaining 1 / 2 is white , what is the total length of the pencil ?
Options: a ) 5 , b ) 3 , c ) 1 , d ) 4 , e ) 2
Rationale: green is 7 / 10 gold is 4 / 5 which can also be written as 8 / 10 white is 1 / 2 which can also be written as 5 / 10 7 / 10 + 8 / 10 + 5 / 10 = 2 answer is e ) 2
Answer: e
Python program:
a = 7 / 10
b = 4 / 5
c = a + b 
d = 1 / 2
e = c + d
Problem: a takes twice as much time as b & c takes thrice as much time as b to finish a piece of work . working together they can finish the work in 18 days . the no . of days need for b to do the work alone is ?
Options: a ) 30 days , b ) 31 days , c ) 33 days , d ) 41 days , e ) 52 days
Rationale: let a takes x days to complete the work , then b takes x / 2 days and c takes 3 x / 2 days to complete the work . a , b and c together complete the work in 18 days in 1 day , all they together can do = > 1 / x + 2 / x + 2 / 3 x = 1 / 18 3 + 6 + 2 / 3 x = 1 / 18 3 x 23 x 2 = 18 x = 66 days the number of days b alone takes to finish the work = x / 2 = 33 days c
Answer: c
Python program:
a = math.lcm(2, 3)
b = a / 1
c = math.lcm(2, 3)
d = c / 2
e = b + d 
f = math.lcm(2, 3)
g = f / 3
h = e + g 
i = h * 18
j = math.lcm(2, 3)
k = i / j
Problem: a man can row his boat with the stream at 20 km / h and against the stream in 8 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 7 kmph , c ) 6 kmph , d ) 5 kmph , e ) 4 kmph
Rationale: "ds = 20 us = 8 s = ? s = ( 20 - 8 ) / 2 = 6 kmph answer : c"
Answer: c
Python program:
a = 20 - 8
b = a / 2
Problem: what will be the compound interest on rs . 25000 after 3 years at the rate of 12 % per annum
Options: a ) rs 10123.20 , b ) rs 10123.30 , c ) rs 10123.40 , d ) rs 10123.50 , e ) none of these
Rationale: "explanation : ( 25000 × ( 1 + 12 / 100 ) 3 ) = > 25000 × 28 / 25 × 28 / 25 × 28 / 25 = > 35123.20 so compound interest will be 35123.20 - 25000 = rs 10123.20 option a"
Answer: a
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: a certain airline ' s fleet consisted of 70 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x be the number of years . 4 x > 70 - 3 x 7 x > 70 x > 10 the answer is e ."
Answer: e
Python program:
a = 3 + 4 
b = 70 / a
Problem: the circumferences of two circles are 264 meters and 352 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 2898 sq m
b ) 1788 sq m
c ) 4312 sq m
d ) 7656 sq m
e ) 1786 sq m
Rationale: let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 264 and 2 ∏ l = 352 s = 264 / 2 ∏ and l = 352 / 2 ∏ difference between the areas = ∏ l 2 - ∏ s 2 = ∏ { 1762 / ∏ 2 - 1322 / ∏ 2 } = 1762 / ∏ - 1322 / ∏ = ( 176 - 132 ) ( 176 + 132 ) / ∏ = ( 44 ) ( 308 ) / ( 22 / 7 ) = ( 2 ) ( 308 ) ( 7 ) = 4312 sq m answer : c
Answer: c
Python program:
a = 2 * math.pi
b = 352 / a
c = circle_area - (
Problem: a man buys rs . 60 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 . 45
Rationale: "dividend on rs . 60 = rs . 9 / 100 x 60 = rs . 5.4 . rs . 12 is an income on rs . 100 . rs . 5.4 is an income on rs . 100 / 12 x 5.4 = rs . 45 . answer : option e"
Answer: e
Python program:
a = 100 / 12
b = 9 / 100
c = b * 60
d = a * c
Problem: a number of 53 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 : 16 * 3 + 1 * 5 = 53 - - > 16 + 1 = 17 . answer : e ."
Answer: e
Python program:
a = 53 / 3
Problem: the rhombus ( afce ) is inscribed in rectangle ( abcd ) . the length of bf = de . if the rectangle has a width of 20 yards and a length of 25 yards , what would be the total length ( the perimeter ) of a fence along the sides defined by afce ?
Options: a ) 80 yards , b ) 82 yards , c ) 84 yards , d ) 85 yards , e ) 90 yards
Rationale: the definition of a rhombus states that every side is of equal length . this definition is the key to solving this question . 1 ) we state that the hypotenuse of either side triangle is x . for this solution , i will be working with the left triangle . 2 ) we state that the bottom and top sides of the rhombus are also x , due to the definition of a rhombus . 3 ) we will define the bottom of the left triangle as y . that is , for the rectangle bottom itself , we can define it as 25 = y + x , where x is a side for the rhombus and y is the bottom part of the left triangle . 4 ) from ( 1 ) , we know that x = 202 + y 2 − − − − − − − √ 202 + y 2 . 5 ) from ( 3 ) , we know x = 25 - y . 6 ) from ( 4 ) and ( 5 ) , we have the equation 202 + y 2 − − − − − − − √ = 25 − y 202 + y 2 = 25 − y 7 ) solving for y , we get 4.5 . 8 ) 25 - 4.5 = 20.5 = x 9 ) since all sides of the rhombus are the same , 20.5 * 4 = 41 * 2 = 82 . the answer is b , 82
Answer: b
Python program:
a = 25 ** 2
b = 20 ** 2
c = a - b
d = 25 * 2
e = c / d
f = 25 - e
g = f * 4
Problem: on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.4 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 2.04 % , b ) 6.12 % , c ) 8 % , d ) 8.25 % , e ) 10 %
Rationale: "if the interest were compounded annually instead of quarterly then in one year the interest would be 2.4 * 4 = 9.6 % . now , since the interest is compounded quarterly then there would be interest earned on interest ( very small amount ) thus the actual interest would be a little bit more than 9.6 % , answer : e"
Answer: e
Python program:
a = 2 * 4
Problem: a can do a piece of work 60 days . b can do work in 20 days . in how many days they will complete the work together ?
Options: a ) 12 days , b ) 16 days , c ) 15 days , d ) 17 days , e ) 18 days
Rationale: "lcm = 60 , ratio = 60 : 20 = 3 : 1 no of days = 60 / ( 3 + 1 ) = 90 / 4 = 15 days answer : c"
Answer: c
Python program:
a = 1 / 60
b = 1 / 20
c = a + b 
d = 1 / c
Problem: if there are 10 apples and 20 oranges , what is the ratio of apples to oranges ?
Options: a ) 10 : 20 , b ) 2 : 4 , c ) 1 : 2 , d ) 4 : 8 , e ) it can not be determined from the information given
Rationale: a ratio should be reduced to the lowest common denominator . 10 : 20 means 10 x : 20 x which can be written as 1 ( 10 ) : 2 ( 10 ) . . . answer : c
Answer: c
Python program:
a = 10 / 20
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 9500 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 700 , d ) rs . 1500 , e ) rs . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 9500 = 38000 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 6000 salary of may is rs . 6500 salary of january = rs . 500 answer : a"
Answer: a
Python program:
a = 8000 * 4
b = 9500 * 4
c = b - 6500
d = a - c
Problem: what two - digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5 ?
Options: a ) 94 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 10 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 10 x ^ 2 + y ^ 2 - 2 xy = 15 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 94 thus the answer is a"
Answer: a
Python program:
a = 10 - 5
b = a + 1 
c = 10 * b
d = c + 5
Problem: last week david spent 20 percent of his wages on recreation . this week , his wages are 30 percent less than last week ʼ s wages and he spent 20 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week
Options: a ) 75 % , b ) 72 % , c ) 70 % , d ) 73 % , e ) 74 %
Rationale: "say david ' s wages last week were $ 100 , so he spent 0.20 * 100 = $ 20 on recreation ; this week ' s wages is 0.70 * 100 = $ 70 , so he spends 0.2 * 70 = $ 14 on recreation ; 14 / 20 = 0.70 , hence the amount he spends on recreation this week is 70 % of the amount he spent on recreation last week : 20 * 0.7 = 14 answer : c"
Answer: c
Python program:
a = 20 / 100
b = 30 / 100
c = 1 - b
d = a * c
e = 20 / 100
f = d / e
g = f * 100
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 180 votes . find the total number of valid votes ?
Options: a ) 450 , 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 = 180 = > 4 x / 10 = 180 = > 4 x = 1800 = > x = 450 . answer : a"
Answer: a
Python program:
a = 100 - 70
b = 70 - a
c = b / 100
d = 180 / c
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 3 . if the can is filled with an additional 10 liters of milk , the can would be full and the ratio of milk and water would become 5 : 2 . find the capacity of the can ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: let c be the capacity of the can . ( 4 / 7 ) * ( c - 10 ) + 10 = ( 5 / 7 ) * c 4 c - 40 + 70 = 5 c c = 30 the answer is d .
Answer: d
Python program:
a = 2 * 10
b = 3 * 5
c = 2 * 4
d = b - c
e = a / d
f = e * 4
g = f + 10 
h = 2 * 10
i = 3 * 5
j = 2 * 4
k = i - j
l = h / k
m = l * 3
n = g + m
Problem: a car runs at the speed of 55 km per hour when not serviced and runs at 90 kmph when serviced . after servicing the car covers a certain distance in 3 hours . how much time will the car take to cover the same distance when not serviced ?
Options: a ) 8 hours , b ) 6 hours , c ) 9 hours , d ) 7 hours 12 minutes , e ) none
Rationale: explanation : time = 90 * 3 / 45 = 6 hours answer â € “ b
Answer: b
Python program:
a = 90 / 2
b = 3 / a
c = 90 * b
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 24 kmph , find the speed of the stream ?
Options: a ) 18 kmph , b ) 6 kmph , c ) 8 kmph , d ) 10 kmph , e ) 12 kmph
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 = 24 / 3 = 8 kmph . answer : c"
Answer: c
Python program:
a = 24 * 2
b = a / 3
c = 24 - b
Problem: a began business with rs . 27000 and was joined afterwards by b with rs . 36000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?
Options: a ) 1.5 , b ) 6.5 , c ) 7.5 , d ) 8 , e ) 2
Rationale: "27 * 12 : 36 * x = 2 : 1 x = 4.5 12 - 4.5 = 7.5 answer : c"
Answer: c
Python program:
a = 4 * 3
b = 4 * 3
c = 27000 * b
d = c / 36000
e = d / 2
f = a - e