## Problem Based on ages

#### Problem Based on ages

1. Two years ago, the ratio of Ram's and Mohan's age was 3 : 2 and at present 7 : 5. What are their present ages?

1. The ratio of Ram's and Mohan's present age is 7 : 5.
Let us assume the present ages of Ram and Mohan are 7Y and 5Y years.

##### Correct Option: A

The ratio of Ram's and Mohan's present age is 7 : 5.
Let us assume the present ages of Ram and Mohan are 7Y and 5Y years.
2 Years ago the age of Ram and Mohan will be 7Y - 2 and 5Y - 2 years.
According to question,
Two years ago, the ratio of Ram's and Mohan's age was 3 : 2, then
(7Y -2)/(5Y - 2) = 3/2
⇒ (7Y -2) x 2 = 3 x (5Y - 2)
⇒ 14Y - 4 = 15Y - 6
∴ Y = 2
Hence, their present ages = 7 x 2 = 14 years and 5 x 2 = 10 year

1. One year ago, the ratio of Yamini and Gamini's was 6 : 7 respectively. Four year hence, the ratio would become 7 : 8. Find the age of Gamini ?

1. Let one year ago the ages of Yamini and Gamini were 6P and 7P years respectively.

##### Correct Option: C

Let one year ago the ages of Yamini and Gamini were 6P and 7P years respectively; then
(6P + 5)/(7P + 5) = 7/8
⇒ (6P + 5) x 8 = 7 x (7P + 5)
⇒ 48P + 40 = 49P + 35
∴ P = 5
Hence, present ago of Gamini = 7P + 1 = 7 x 5 + 1 = 36 years

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