Olympiad topic · P1–P4
Age problems
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.
Try one
★★ MediumThis year the older sister is 9 and the younger sister is 2.
In how many years will their ages add up to 49?
- 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?
- 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.
Answer: 19 years
Four levels, step by step
- ★EasyFree2 question types · unlimited questionsHow differences and totals change.
- ★★MediumFree2 question types · unlimited questionsWhen one age is a multiple of another.
- ★★★HardFree2 question types · unlimited questionsMultiples at two different times, or "when I was your age".
- ★★★★Expert (competition level)VIP2 question types · unlimited questionsSeveral people, or years before a child was born.
Age problems: what it is and how to solve it
Problems about people's ages: years later or earlier, what their total, difference or multiple becomes.
For example: Dad is 32 and his son 5. In how many years will Dad be 4 times as old? They're always 27 years apart, so the son will be 27 ÷ (4 − 1) = 9: in 4 years.
The key idea: Two people's age difference never changes; each year everyone gets 1 older, so three people's total grows by 3. Hold on to the fixed difference and it becomes a difference-and-times problem. The usual method at school uses an equation: in x years, 32 + x = 4(5 + x).
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