Question

The ratio of the ages of a mother and her daughter is 4 : 1.

In 4 years, the ratio of the sum of their ages to the age of the daughter is 4 : 1. Find their current ages.

Answer 1

Answer:

Given:

Ratio of present ages of mother and daughter = 5 : 1

Ratio of ages of mother and daughter after 6 years = 3 : 1

Concept Used:

The difference between ages of two persons at any time is constant.

Calculation:

Let the present ages of Mother and Daughter be 5x and x

After 6 years their ages will be 5x + 6 and x + 6

According to the question-

(5x + 6)/(x + 6) = 3/1

⇒ 5x + 6 = 3x + 18

⇒ x = 6

∴ The present age of daughter is 6 years

sorry i gave 5:1 please change it . i dint understand your solution so i changed the number.hope u understand

Answer 2

10 years ago, respective ratio of the age of mother and daughter was 4 : 1. 10 years hence, the respective ratio of the age of mother and daughter will become 2 : 1. At present, what is the sum of their age?

Solution: Let the present age of the mother be M and that of the daughter, D.

Ten years ago the ratio of their ages was

(M-10):(D-10) = 4:1

4D-40 = M-10, or

M = 4D-30 …(1)

Ten years hence the ratio of their ages will be

(M+10):(D+10) = 2:1

2D+20 = M+10, or

M = 2D+10 …(2)

Equate (1) and (2): 4D-30 = 2D+10, or

2D = 40, or D = 20 and so M = 50.

The sum of their ages at present is 70 years.