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Nanyang 2025 P6 Maths Prelim — Paper 2 Q14a Solution

Paper 2 · Q14a · 3 marks · Ratio

Question

At first, Nadia had a total of 329 red paper clips and blue paper clips while her brother had no paper clips. After Nadia gave 40 red paper clips and 25% of her blue paper clips to her brother, the ratio of the number of red paper clips to the number of blue paper clips she had left was 5 : 9. How many blue paper clips did Nadia give to her brother?
Answer: 51

Worked solution

  1. Let Nadia's blue clips at first $= b$, red $= 329 - b$. She gave away $40$ red and $25\%$ of blue, keeping $75\%$ of blue. Red left $= 329 - b - 40 = 289 - b$. Blue left $= 0.75b$. $\frac{289 - b}{0.75b} = \frac{5}{9}$, so $9(289 - b) = 5 \times 0.75b$
  2. $2601 - 9b = 3.75b$
  3. $2601 = 12.75b$
  4. $b = 204$. Blue given away $= 25\% \times 204 = 51$.

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