Mr Manu is 4 times as old as his son, Adu. 7 years ago the sum of their ages was 76. How old is Adu?

Analyze the question: Manu's age is 4 times Adu's age now. Seven years ago, the sum of their ages was 76. We need Adu's present age.

Concept: Let Adu's present age be x, so Manu's present age is 4x. Seven years ago, each person was 7 years younger, so subtract 7 from each age.

Solution:

Seven years ago:

• Adu: x − 7
• Manu: 4x − 7

Sum of their ages: (x − 7) + (4x − 7) = 76 5x − 14 = 76 5x = 90 x = 18

Check: Adu is 18 and Manu is 72. Seven years ago they were 11 and 65, and 11 + 65 = 76. ✓

Tip: In age problems, when the question refers to the past, subtract the number of years from each person. So the total drops by 7 × 2 = 14. You can shortcut this by saying the present sum is 76 + 14 = 90, and since the ages are in ratio 1:4 (5 parts), Adu = 90 ÷ 5 = 18.