The ratio of Ali's father's age to Ali's age now is 7 : 2. In 6 years' time, the ratio of their ages will be 8 : 3. How old is Ali now?
Try it yourself · watch the animation →Draw the models for now and 6 years later. The age difference does not change with time.
Answer: Ali now 12 years old
Method: In age problems, the age difference stays constant. Compare the difference in the two ratios using bar models, then use the number of years passed to find 1 unit.
12 years old — Now: Mother : Mei Ling = 4 : 1, so the gap is 3 units. In 12 years' time: 5 : 2, also a gap of 3 units. The age difference is constant, so 1 unit is the same number of years. Mei Ling changes from 1 unit to 2 units, so the increase of 1 unit = 12 years. Mei Ling now = 1 × 12 = 12 years old.
12 years old — The current gap is 5 − 3 = 2 present units. In 4 years' time, the gap is 3 − 2 = 1 future unit. Since the age difference is constant, 2 present units = 1 future unit. Raju in 4 years' time is 2 future units = 4 present units. Raju now is 3 present units. The increase of 1 present unit = 4 years, so Raju now = 3 × 4 = 12 years old.
42 years old — The current gap is 7 − 2 = 5 present units; the later gap is 5 − 2 = 3 future units. The age difference is constant, so 5 present units = 3 future units. Split this same gap into 15 small parts: 1 present unit = 3 small parts, and 1 future unit = 5 small parts. Ali now is 2 present units = 6 small parts; in 8 years' time, he is 2 future units = 10 small parts. The increase of 4 small parts = 8 years. 1 small part = 2 years. Father now is 7 present units = 21 small parts = 42 years old.
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