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Maths olympiad question · P1–P2★ Easy

Age problems: olympiad question 1

An easy question on age problems for P1–P2, with a step-by-step solution, diagrams and the answer. Age problems are common in the Hua Xia Cup's P1 to P4 first and qualifying rounds, and rarer in the P5 and P6 papers.

The question

This year Mum is 31 and Ming is 3.

In 19 years, how much older than Ming will Mum be?

Show the hints (2)
  1. Hint 1: Each year, how much older do Mum and Ming each get?
  2. Hint 2: Both get 1 year older every year. Does the gap between them change?

Worked solution

Have a go first, then read the solution step by step.

  1. 1.This year Mum is 31 − 3 = 28 years older than Ming.
  2. 2.Every year both get 1 year older. In 19 years both are 19 years older, so the gap is still 28.
  3. ⚠️Common mistake: adding 19 to one of them only. Both get 19 years older.

Answer: 28 years

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