## Problem Based on ages

#### Problem Based on ages

1. The ages of Surabhi and Neerja are in the ratio of 6 : 7 respectively. After 6 years the ratio of their ages will be 15 : 17. Find the age of Neerja.

1. Let the present ages of Surabhi and Neerja are 6x and 7x years respectively.

##### Correct Option: C

Let the present ages of Surabhi and Neerja are 6x and 7x years respectively.
According to question,
(6x + 6)/(7x + 6) = 15/17
⇒ (6x + 6)x17 = 15x(7x + 6)
⇒ 102x + 102 = 105x + 90
⇒ 3x = 12
∴ x = 4
Hence, present ages of Neerja = 7 x 4 = 28 years

1. The average age of a woman and her daughter is 42 years. The ratio of their ages is 2 : 1 respectively. Find the daughter's age.

1. Let the present ages of womon and her daugher be 2x and x years respectively .

##### Correct Option: B

Let us assume the present ages of woman and her daughter be 2x and x years respectively ; then
According to question,
The average age of a woman and her daughter is 42 years
(2x + x)/2 = 42
⇒ 3x = 84
∴ x = 28
Hence, present age of her daughter = 28 years

1. The ages of A and B are in the ratio of 11 : 13 respectively. After 7 years the ratio of their ages will be 20 : 23. What is the difference in years between their ages?

1. Let the present ages of A and B are 11x and 13x years respectively.

##### Correct Option: C

Let the present ages of A and B are 11x and 13x years respectively; then
According to question,
After 7 years the ratio of their ages will be 20 : 23.
(11x + 7 ) / (13x + 7) = 20/23
⇒ (11x + 7 ) 23 = 20 (13x + 7)
⇒ 253x + 161 = 260x + 140
⇒ 7x = 21
∴ x = 3
Hence, difference of their ages = 13x - 11x = 2x = 2 x 3 = 6 years

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