Today’s problem — free all day, every step. Every day has one.
Wei and his father — a changing age ratio
The ratio of Wei's age to his father's age is 1 : 4. The difference between their ages is 30 years. In how many years will the ratio of Wei's age to his father's age be 2 : 5?
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10 years.
The pattern behind it: Constant difference
The gap between the two amounts never changes.
In this one. An age gap is fixed for life, so the difference is the quantity to measure both ratios against — 3 units then, 3 parts now, the same 30 years.
How to spot it
Both amounts go up or down by the same amount. Ages are the common case, because the same number of years passes for both people.
Common mistake
Children treat the gap as fixed when only one person changed, forgetting that adding to one person alone moves the gap by exactly that amount.
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.