Question

a boy is three years younger than his sister. two years ago he was two-thirds of his sister's age. what are their present ages ​

Answer 1

Answer:

The boy: 8 years old

The sister: 11 years old

Explanation:

We assume that the age at present of the boy is x (years old).

As he is younger than his sister 3 years, so that his sister's present age is great than x 3 years

=> Her present age is: x + 3 (years old)

Two years ago, the boy is younger than present two years

=> The boy's age two years ago is: x - 2 (years old)

Similarly, the sister's age two years ago is: (x+3)-2 = x + 1 (years old)

As given, two years ago he was two-thirds of his sister's age, so that we have:

The boy's age two years ago = $\frac{2}{3}$ × the sister's age two years ago

⇒ $x - 2 = \frac{2}{3}(x+1)$

⇒ $x - 2 = \frac{2}{3}x + \frac{2}{3}$

⇒ $x - \frac{2}{3}x = \frac{2}{3} + 2$

⇒ $\frac{1}{3} x = \frac{8}{3}$

⇒ $x = \frac{8}{3}. 3 = 8$

=> x + 3 = 8 + 3 = 11

So the present age of the boy is 8 years old, of the sister is 11 years old