The ratio of copper and zinc in a 63 kg alloy is 4: 3. Some amount of copper is extracted from the alloy, and the ratio becomes 10: 9. How much copper is extracted?
Answer & explanation
Correct answer: option 2
The initial alloy weighs 63 kg and the ratio of Copper : Zinc = 4 : 3.
Find the initial quantities
Total parts = $4 + 3 = 7$
- Copper = $\frac{4}{7} \times 63 = 36 \text{ kg}$
- Zinc = $\frac{3}{7} \times 63 = 27 \text{ kg}$
Let $x$ kg of copper be extracted
Then:
- Copper left = $36 - x \text{ kg}$
- Zinc remains = $27 \text{ kg}$
Given the new ratio is 10 : 9:
$\frac{36 - x}{27} = \frac{10}{9}$
Cross multiply:
$9(36 - x) = 270$
$324 - 9x = 270$
$9x = 54$
$x = 6$