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Ai Tong 2025 P6 Maths Prelim — Paper 1 Booklet A Q15 Solution

Paper 1 Booklet A · Q15 · 2 marks · Ratio

Question

4 years ago, the ratio of Calvin's age to Lina's age was 2 : 7. In 8 years' time, Calvin's age will be $\frac{2}{5}$ of Lina's age. How old is Calvin now?

1. 10 years old
2. 18 years old
3. 22 years old
4. 30 years old

Answer: 3

Worked solution

$\text{4 years ago: Calvin} = 2u,\ \text{Lina} = 7u$
$\text{In 8 years: Calvin} = 2u + 12,\ \text{Lina} = 7u + 12$
$2u + 12 = \frac{2}{5}(7u + 12)$
$5(2u + 12) = 2(7u + 12)$
$10u + 60 = 14u + 24$
$4u = 36$
$u = 9$
$\text{Calvin now} = 2(9) + 4 = 22 \text{ years old}$

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