Question

50 kg of an alloy of lead and tin contains 60% of lead .how much lead must be melted into it to make the alloy contain 75% of lead

Answer 1

Quantity of lead in 50 kg of alloy = 60% of 50 kg = $(50 \times \frac{60}{100})$ kg = 30 kg.

Let the required quantity of lead to be added be x kg.

Then, weight of lead = (30 + x) kg.

And, weight of new alloy = (50 + x) kg.

Percentage of lead in new alloy = $[\frac{(30 + x)}{(50 + x)} \times 100]$ %

∴ $\frac{30 + x}{50 + x} \times 100 = 75$

⇒ $\frac{(30 + x)}{(50 + x)} =\frac{75}{100}$

⇒ $\frac{(30+x)}{(50+x)} =\frac{3}{4}$

⇒ 4(30 + x) = 3(50 + x)

⇒ 120 + 4x = 150 + 3x

⇒ 4x - 3x = 150 - 120

⇒ x = 30

∴ quantity of lead to be added = 30 kg.

Answer 2

Answer:

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