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
Dad is 39 this year and his son is 12.
In how many years will Dad be exactly twice his son's age?
Show the hints (2)
💡Hint 1: What is the age gap? Does it ever change?
💡Hint 2: When Dad is twice as old, call the son's age then one part; Dad is 2 parts. How many parts is the gap?
Worked solution
Have a go first, then read the solution step by step.
1.Dad is 39 − 12 = 27 years older than his son, and that gap never changes.
2.When Dad is twice as old, the son is 1 part and Dad 2 parts: 1 part = 27, so the son is 27 ÷ 1 = 27 then.
3.The son goes from 12 now to 27: 27 − 12 = 15, so in 15 years.
⚠️Common mistake: answering the son's age then, 27. The question asks how many years from now.
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