mathschallenge.net

Problem

Sarah started school at the age of five. She spent one quarter of her life being educated, and went straight into work. After working for one half of her life, she lived for fourteen happy years after retiring.

How old was she when she retired?

Solution

As Sarah spent $\frac{1}{4} + \frac{1}{2} = \frac{3}{4}$ of her life between school and work, the five years before school and fourteen years after retiring must be $\frac{1}{4}$ of her life.

That is, she lived for $4 \times 19 = 76$ years, and so she retired when she was $76 - 14 = 62$ years old.