A medium question on age problems for P2–P3, 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 the older sister is 9 and the younger sister is 2.
In how many years will their ages add up to 49?
Show the hints (2)
💡Hint 1: Each year, how much does the total of their ages go up?
💡Hint 2: The total has to grow from this year's to 49. By how much?
Worked solution
Have a go first, then read the solution step by step.
1.This year the total is 9 + 2 = 11.
2.Later both have grown by the same number of years (orange). The total must grow from 11 to 49, so the two orange pieces make 49 − 11 = 38.
3.Each year both get 1 older, so the total grows by 2: 38 ÷ 2 = 19, so in 19 years.
⚠️Common mistake: thinking the total grows by 1 a year and answering 38.
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