## Problem Based on ages

#### Problem Based on ages

1. The average age of A, B and C is 25 years. The ratio of their age is 3 : 5 : 7. What is the age of A?

1. Let the present ages of A, B and C are 3x, 5x and 7x years respectively;

##### Correct Option: B

Let the present ages of A, B and C are 3x, 5x and 7x years respectively; then
According to question,
3x + 5x + 7x = 3 x 25
⇒ 15x = 75
∴ x = 5
Hence, age of A = 3x = 3 x 5 = 15 years

1. Three years ago, the average age of a family of five members was 17 years. A baby having been born, the average age of the family is the same as what was three years ago. The present age of the baby is:

1. Let us assume the present age of baby Y year.

##### Correct Option: D

Let us assume the present age of baby Y year.
According to question,
Three years ago, the average age of a family of 5 members was 17 years.
The present Total age of the family of 5 member = 5 x 17 + 5 x 3 =100 ..........(1)
Again according to question,
The average age of the family is the same as what was three years ago.
The present average age of family of 6 member= 17
Total present age of family of 6 member / 6 = 17
(Total present age of family of 5 member + present age of baby)/6 = 17
100 + Y = 17 x 6
Y = 17 x 6 - 100 = 102 - 100 = 2 years

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 ratio of ages of A and B is 3 : 11. After 3 years the ratio becomes 1:3. What are the ages of A and B?

1. Let us assume the the ages of A and B be 3x and 11x years.

##### Correct Option: A

Let us assume the ages of A and B be 3x and 11x years; then
After 3 years the ages of A and B will be 3x + 3 and 11x + 3.
According to question,
After 3 years the ratio of the ages becomes 1: 3,
(3x + 3)/(11x + 3) = 1/3
⇒ 3 (3x + 3) = 1 (11x + 3)
⇒ 9x + 9 = 11x + 3
⇒ 2x = 6
∴ x = 3
Hence, their present age, 3x = 3 x 3 = 9 years; 11x = 11 x 3 =33 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