Question 1

The sum of two number is 29 and the difference of their squares is 145. The difference between the number is?

Accepted Answer

Let the number be a and b Then, (a-b) = (a2 - b2) / a+b = 145/29 = 5

Question 2

The difference of two number is 5 and the difference of their squares is 135. The sum of the number is?

Accepted Answer

Let the number be a and b. Then, (a + b) = (a2 -b2) / (a-b) = 135/5 = 27

Question 3

If 1 is added to the denominator of fraction, the fraction becomes 1/2. If 1 is added to the numerator, the fraction becomes 1. The fraction is?

Accepted Answer

Let the required fraction be x/y Then, x/(y + 1) = 1/2 ⇒ 2x - y = 1 ...(1) (x + 1) / y = 1 ⇒ x - y = -1 ...(2) Solving Eq. (1) and (2) We get x = 2, y = 3 ∴ The fraction is 2/3

Question 4

4/5 of a number exceeds its 2/3 by 8. The number is?

Accepted Answer

Let the number be x, Then, 4x/5 - 2x/3 = 8 ⇒ (12x - 10x) / 15 = 8 ⇒ 2x = 120 ∴ x = 60

Question 5

If one-fourth of one-third of one-half of a number is 15, the number is?

Accepted Answer

Let the number be N . Then, 1/4 of 1/3 of 1/2 of N = 15 ⇒ 1/4 x 1/3 x 1/2 x N = 15 ⇒ N/24 = 15 ⇒ N = 24 x 15 = 360 .

Question 6

A number whose fifth part increased by 5 is equal to its fourth part diminished by 5 is?

Accepted Answer

Let the number be N. Then, (N/5) + 5 = (N/4) - 5 ⇒ (N/4) - (N/5) = 10 ⇒ (5N - 4N)/20 = 10 ∴ N = 200

Question 7

The product of two numbers is 120. The sum of their squares is 289. The sum of the two numbers is?

Accepted Answer

Let the number be a and b . Then, (a+b)2 = a2 + b2 + 2ab = 289 + 2 x 120 = 289 + 240 = 529 ∴ a+b = √529 = 23

Question 8

The sum of squares of two numbers is 80 and the square of their difference is 36. The product of the two numbers is?

Accepted Answer

Let the number be a and b. Then, a2 + b2 = 80 and (a - b)2= 36 ⇒ a2 + b2 - 2ab = 36 ⇒ 2ab = (a2 + b2)-36 = 80 - 36= 44 ∴ Product = ab = 22

Question 9

The sum of two number is twice their difference, If one of the number is 10, the other number is?

Accepted Answer

Let the other number be x. Then, 10 + x = 2(x - 10) ⇒ x = 30

Question 10

4/5 of a certain number is 64, Half of that number is?

Accepted Answer

Let the number be N, Then 4N/5 = 64 ⇒ N = 64 x 5/4 = 80 ∴ Half of the number = 80/2 = 40

Question 11

Three - fourth of number is more than two-third of the number by 5. The number is?

Accepted Answer

Let the number be N. Then, 3N/4 - 2N/3 = 5 ⇒ (9N - 8N) / 12 = 5 ∴ N = 60

Question 12

What number must be added to numerator and denominator of 3/4 to give 11/12?

Accepted Answer

Let (3 + x)/ (4 + x) = 11/12. Then, 12(13 + x) = 11 (4 + x) ⇒ x = 44 - 36 = 8

Question 13

Three number are in the ratio 4 : 5 : 6 and their average is 25. The largest number is?

Accepted Answer

Let the number be 4N, 5N and 6N Then, 4N + 5N + 6N/3 = 25 or 15N = 75 or N = 5 Then largest number = 6N = 6 x 5 = 30

Question 14

The sum of three consecutive odd number is 57. The middle one is?

Accepted Answer

Let the requirement odd integers be N, N +2 and N + 4 Then, N + (N + 2) + (N + 4) = 57 ⇒ 3N = 51 ⇒ N = 17 ∴ The integers are 17, 19, 21.

Question 15

A number when divided by 6 is diminished by 40. The number is?

Accepted Answer

Let the required number be N, Then, N/6 = N - 40 ⇒ N + 240 = 6N ∴ N = 48.

Question 16

Divide 50 into two parts so that the sum of their reciprocals is 1/12?

Accepted Answer

Let the number be N and (50 - N) Then, 1/N + 1/(50-N) = 1/12 ⇒ (50 - N + N) / {N(50 - N)} = 1/12 ⇒ N2 - 50N + 600 = 0 ⇒ N = 30 or 20 ∴ the number are 20, 30

Question 17

The ratio between two numbers is 2 : 3. If the consequent is 24, the antecedent is?

Accepted Answer

Let the antecedent be N. Then, N/24 = 2/3 ⇒ N = (24 x 2) / 3 = 16

Question 18

If a number is subtracted from the square of its one half, the result is 48. The square root of the number is?

Accepted Answer

Let the number be N. Then (N/2)2 - N = 48 ⇒ N2/4 - N = 48 ⇒N2 - 4N-192= 0 ⇒ (N-16) (N+12) = 0 ⇒ N = 16 ∴ The square root of the number is 4.

Question 19

The sum of three consecutive number is given. What is the difference between first and third number?

Accepted Answer

Let the three consecutive numbers be x, x+1 and x+2 respectively ∴ Diff between first and third numbers = (x + 2) - x = 2

Question 20

A number gets reduced to its one-third, when 48 is subtracted from it. What is two-third of that number?

Accepted Answer

Let the number be N. Then, N - N/3 = 48 2N/3 = 48.

Number System Questions