Question 1

A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes?

Accepted Answer

Number of cuts made to cut a roll into 10 pieces = 9. Therefore Required number of rolls = (45 x 24)/9 = 120.

Question 2

A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether?

Accepted Answer

Since each pole at the corner of the plot is common to its two sides, so we have : Total number of poles needed = 27 x 4 - 4 = 108 - 4 = 104.

Question 3

Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today?

Accepted Answer

Let Varan's age today = x years. Then, Varan's age after 1 year = (x + 1) years. Therefore x + 1 = 2 (x - 12) ⟺ x + 1 = 2x - 24 ⟺ x = 25.

Question 4

In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?

Accepted Answer

Let the number of boys be x. Then, (3/4)x = 18 or x = 18 x(4/3) = 24. If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36. Therefore Number of girls in the class = (36 - 24) = 12.

Question 5

An institute organised a fete and 1/5 of the girls and 1/8 of the boys participated in the same. What fraction of the total number of students took part in the fete?

Accepted Answer

Data inadequate

Question 6

Mr. Johnson was to earn £ 300 and a free holiday for seven weeks' work. He worked for only 4 weeks and earned £ 30 and a free holiday. What was the value of the holiday?

Accepted Answer

Question 7

A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B…

Accepted Answer

Clearly, we have : B-3 = E ...(i) B + 3 = D ...(ii) A+B = D + E+10 ...(iii) B = C + 2 ...(iv) A+B + C + D + E= 133 ...(v) From (i) and (ii), we have : 2 B = D + E ...(vi) From (iii) and (vi), we have : A = B + 10 ...(vii) Using (iv), (vi) and (vii) in (v), we get: (B + 10) + B + (B - 2) + 2B = 133 ⟺ 5B = 125 ⟺ B = 25.

Question 8

Three friends had dinner at a restaurant. When the bill was received, Amita paid 2/3 as much as Veena paid and Veena paid 1/2 as much as Tanya paid. What faction of the bill did Veena pay?

Accepted Answer

Question 9

In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is

Accepted Answer

Each row contains 12 plants. There are 11 gapes between the two corner trees (11 x 2) metres and 1 metre on each side is left. Therefore Length = (22 + 2) m = 24 m.

Question 10

The number of boys in a class is three times the number of girls. Which one of the following numbers cannot represent the total number of children in the class?

Accepted Answer

Let number of girls = x and number of boys = 3x. Then, 3x + x = 4x = total number of students. Thus, to find exact value of x, the total number of students must be divisible by 4.

Question 11

In a class, 20% of the members own only two cars each, 40% of the remaining own three cars each and the remaining members own only one car each. Which of the following statements is definitely true from the given statements?

Accepted Answer

Let total number of members be 100, Then, number of members owning only 2 cars = 20. Number of members owning 3 cars = 40% of 80 = 32. Number of members owning only 1 car = 100 - (20 + 32) = 48. Thus, 48% of the total members own one car each.

Question 12

At a dinner party every two guests used a bowl of rice between them, every three guests used a bowl of dal between them and every four used a bowl of meat between them. There were altogether 65 dishes. How many guests were present at the party?

Accepted Answer

Question 13

The total number of digits used in numbering the pages of a book having 366 pages is

Accepted Answer

Total number of digits = (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.) = (1 x 9 + 2 x 90 + 3 x 267) = (9 + 180 + 801) = 990.

Question 14

Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start?

Accepted Answer

L.C.M. of 6, 5, 7, 10 and 12 is 420. So, the bells will toll together after every 420 seconds i.e. 7 minutes. Now, 7 x 8 = 56 and 7 x 9 = 63. Thus, in 1-hour (or 60 minutes), the bells will toll together 8 times, excluding the one at the start.

Question 15

In a cricket match, five batsmen A, B, C, D and E scored an average of 36 runs. D Scored 5 more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them. How many runs did E score?

Accepted Answer

Total runs scored = (36 x 5) = 180. Let the runs scored by E be x. Then, runs scored by D = x + 5; runs scored by A = x + 8; runs scored by B = x + x + 5 = 2x + 5; runs scored by C = (107 - B) = 107 - (2x + 5) = 102 - 2x. So, total runs = (x + 8) + (2x + 5) + (102 - 2x) + (x + 5) + x = 3x + 120. Therefore 3x + 120 =180 ⟺ 3X = 60 ⟺ x = 20.

Question 16

In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family?

Accepted Answer

Let d and s represent the number of daughters and sons respectively. Then, we have : d - 1 = s and 2 (s - 1) = d. Solving these two equations, we get: d = 4, s = 3.

Question 17

A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum." The woman's age is

Accepted Answer

Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age. Then, woman's age = (10X + y) years; husband's age = (10y + x) years. Therefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y) ⟺ (9y-9x) = (1/11)(11y + 11x) = (x + y) ⟺ 10x = 8y ⟺ x = (4/5)y Clearly, y should be a single-digit multiple of 5, which is 5. So, x = 4, y = 5. Hence, woman's age = 10x + y = 45 years.

Question 18

The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago?

Accepted Answer

Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years.

Question 19

A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair?

Accepted Answer

Since there are socks of only two colours, so two out of any three socks must always be of the same colour.

Question 20

What is the product of all the numbers in the dial of a telephone?

Accepted Answer

Since one of the numbers on the dial of a telephone is zero, so the product of all the numbers on it is 0.

Arithmetic Reasoning Questions