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Nanyang 2025 P6 Maths Prelim — Paper 2 Q8 Solution

Paper 2 · Q8 · 3 marks · Fractions and Decimals

Question

Mr Soh spent $\frac{1}{5}$ of his money on a pair of shoes and $\frac{3}{4}$ of his remaining money on a bag, a shirt and a hat. The bag cost 3 times as much as the hat. The shirt cost $\frac{1}{2}$ as much as the hat. The pair of shoes cost $\$48$ more than the shirt. How much money did Mr Soh have at first?
Answer: $360

Worked solution

  1. Let total money $= 20$ units. Shoes $= \frac{1}{5} \times 20 = 4$ units. Remaining $= 16$ units. Spent on bag, shirt, hat $= \frac{3}{4} \times 16 = 12$ units. Let the hat $= 2$ parts
  2. bag $= 6$ parts
  3. shirt $= 1$ part
  4. total $= 9$ parts $= 12$ units. The shirt $= \frac{1}{9} \times 12 = \frac{4}{3}$ units. Shoes $-$ shirt $= 4 - \frac{4}{3} = \frac{8}{3}$ units $= \$48$, so $1$ unit $= \$18$. Total $= 20 \times \$18 = \$360$.

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