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 = [tex]\frac{2}{3}[/tex] × the sister's age two years ago
⇒ [tex]x - 2 = \frac{2}{3}(x+1)[/tex]
⇒ [tex]x - 2 = \frac{2}{3}x + \frac{2}{3}[/tex]
⇒ [tex]x - \frac{2}{3}x = \frac{2}{3} + 2[/tex]
⇒ [tex]\frac{1}{3} x = \frac{8}{3}[/tex]
⇒ [tex]x = \frac{8}{3}. 3 = 8[/tex]
=> x + 3 = 8 + 3 = 11
So the present age of the boy is 8 years old, of the sister is 11 years old
