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

The boy: 8 years old

The sister: 11 years old

Step-by-step 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 =
`(2)/(3)` × the sister's age two years ago

⇒
`x - 2 = (2)/(3)(x+1)`

⇒
`x - 2 = (2)/(3)x + (2)/(3)`

⇒
`x - (2)/(3)x = (2)/(3) + 2`

⇒
`(1)/(3) x = (8)/(3)`

⇒
`x = (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