## Problem Based on ages

#### Problem Based on ages

1. Present age of Rahul is 5 years less than Ritu's present age. If 3 years ago Ritu's age was x years, which of the following represents Rahul's present age in years?

1. 3 Years age Ritu's age was x years, then
Ritu's present age = x + 3 years

##### Correct Option: A

3 Years age Ritu's age was x years, then
Ritu's present age = x + 3 years
According to question,
Present age of Rahul is 5 years less than Ritu's present age
Hence, present age of Rahul = x + 3 - 5 = x - 2 years

1. The present age of Sanyal is 3 times the present age of his son. Six years hence, the ratio of their ages will be 5 : 2 respectively. The present age of Sanyal is:

1. Let us assume the present age of son be x then his father present age will be 3x.

##### Correct Option: C

Let us assume the present age of son be x then his father present age will be 3x.
According to question,
Six years hence, the ratio of their ages will be 5 : 2 respectively
(3x + 6)/(x+6) = 5/2
⇒ (3x + 6)2 = 5(x+6)
⇒ 6x + 12 = 5x + 30
∴ x = 18
Hence, age of Sanyal = 3 x 18 = 54 years

1. The ratio of ages of Namrata and Divya is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 4 years will be:

1. Let the present ages of Namrata and Divya are 4x and 3x years.

##### Correct Option: B

Let the present ages of Namrata and Divya are 4x and 3x years respectively; then
According to question,
4x + 3x = 28
∴ x = 4
Hence, their present ages are 16 and 12 years.
So required ratio = (16 +4) : (12 + 4) = 20 : 16 = 5 :4

1. At present, the ratio between the ages of Gopal and Madhawa is 4 : 3. After 6 years, Gopal's age will be 26 years. The present age of Madhwa is:

1. Let the present age of Gopal and Madhawa are 4x and 3x years respectively.

##### Correct Option: C

Let the present age of Gopal and Madhawa are 4x and 3x years respectively; then
According to question,
4x + 6 = 26
⇒ 4x = 20
∴ x = 5
Hence, present age of Madhawa = 3x = 3 x 5 = 15 years

1. The sum of the ages of Ram, Shyam and Mohan is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. The present age of Mohan is:

1. Let us assume 10 years ago, ages of Ram, Shyam and Mohan were 2x, 3x and 4x years respectively.

##### Correct Option: A

Let us assume 10 years ago, ages of Ram, Shyam and Mohan were 2x, 3x and 4x years respectively.
Present ages of Ram, Shyam and Mohan will be 2x + 10 , 3x + 10 and 4x + 10 years.
According to question,
2x + 10 + 3x + 10 + 4x + 10 = 93
⇒ 9x + 30 = 93
⇒ 9x = 93 - 30
⇒ 9x = 63
⇒ x = 7
The present age of mohan = 4x + 10 = 4x7 + 10 = 38 years