Question

A mother’s age is six times her daughter’s age. Four years from now, the age of the mother will be four times her daughter’s age. The present age (in years) of the mother and the daughter respectively are ___.

• A. 60 years, 10 years
• B. 36 years, 6 years
• C. 30 years, 5 years
• D. 24 years, 4 years

Answer 1

The correct option is B 36 years, 6 years

Let x years and y years represent the age of the mother and the daughter respectively.

Then, we have x = 6y------------>(1)

Four years from now, the mother's age will be (x + 4) years and the daughter's age will be (y + 4) years.

Thus, we have x + 4 = 4(y + 4)

$⟹$x – 4y = 12---------->(2)

Substituting the value of x from (1) in (2), we have

6y – 4y = 12

$⟹$ 2y = 12

$⟹$ y = 6

Since x = 6y, we have x = 36

Hence, the present age of the mother and the daughter are 36 years and 6 years respectively.