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ACS Junior 2025 P6 Maths Prelim — Paper 1 Booklet A Q11 Solution

Paper 1 Booklet A · Q11 · 2 marks · Ratio

Question

A plank of wood was first cut into two pieces in the ratio 2 : 3. The longer piece was then cut into 2 pieces in the ratio 1 : 3. The shortest piece of wood among the three pieces was 18 cm long. What was the length of the original plank of wood?
Answer: 4

Worked solution

  1. \text{Plank cut } 2:3 \to \text{ pieces of } 2u, 3u
  2. \text{Longer piece (3u) cut } 1:3 \to \frac{3u}{4}, \frac{9u}{4}
  3. \text{Three pieces: } 2u, \frac{3u}{4}, \frac{9u}{4}
  4. \text{Shortest} = \frac{3u}{4} = 18
  5. u = 24
  6. \text{Total length} = 5u = 120 \text{ cm}

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