The difference in age between a girl and her younger sister is 4 years. The younger sister in turn is 4 years older than her brother. The sum of the ages of the younger sister and her brother is 16. How old are the three children?

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Solution

Let the age of the girl = 'x' years.
So, the age of her younger sister = (x $-$ 4) years.
Thus, the age of the brother = (x $-$ 4 $-$ 4) years = (x $-$ 8) years.
ATQ:
⇒ (x $-$ 4) + (x $-$ 8) = 16
⇒ x + x $-$ 4 $-$ 8 = 16
⇒ 2x $-$ 12 = 16
Adding 12 to both sides, we get
⇒ 2x $-$ 12 + 12 = 16 + 12
⇒ 2x = 28
Dividing both sides by 2, we get
⇒ $\frac{2 x}{2} = \frac{28}{2}$
⇒ x = 14
Thus, the age of the girl = x = 14 years, the age of the younger sister = x $-$ 4 = 14 $-$ 4 = 10 years,
and the age of the younger brother = x $-$ 8 = 14 $-$ 8 = 6 years.

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