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

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Quantity of lead in 50 kg of alloy = 60% of 50 kg

$= (50 \times \frac{60}{100} )kg = 30kg.$

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

The , 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 = 30kg .