# 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 the brother is 16. How old are the three children?

**Given :**

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 the brother is 16.

**To do :**

We have to find the ages of the children.

**Solution :**

Let the age of the younger sister be x

This implies,

The age of the girl $= x+4$

The age of the brother $= x-4$

The sum of the ages of the younger sister and her brother $= 16$

Therefore,

$x+(x-4) = 16$

$2x-4 = 16$

$2x = 16+4$

$2x=20$

$x=\frac{20}{2}$

$x=10$

**The age of the younger sister is 10 years.**

**The age of the younger brother is $10-4=6$ years.**

**The age of the girl is $10+4=14$ years.**

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