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?

6 Kg

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:

$9(36 - x) = 270$

$324 - 9x = 270$

$9x = 54$

$x = 6$