A mixture of 750 kg of alloy of copper and tin contains 25% tin. How much tin must be added so that it becomes 70% of the mixture?

The correct option is 1125 kg.

Let us solve this problem step-by-step to find out how much tin needs to be added to the mixture.

Step 1: Find the initial amounts of copper and tin in the alloy.

The total initial mass of the alloy mixture = 750 kg.

The mixture contains 25% tin. Therefore, the remaining 75% of the mixture must be copper.

Amount of tin initially present:

$\text{Initial tin}=25\%\text{ of }750\text{ kg}=\frac{25}{100}\times 750=187.5\text{ kg}$

Amount of copper initially present:

$\text{Initial copper}=750-187.5=562.5\text{ kg}$

Step 2: Set up the equation for adding tin.

Let the amount of tin to be added be $x$ kg.

When $x$ kg of pure tin is added:

• The new total mass of the mixture becomes $(750+x)$ kg.

• The new total mass of tin becomes $(187.5+x)$ kg.

We are given that tin must make up 70% of the new mixture. Thus, copper will make up 30% of the new mixture.

Using the percentage of tin in the new mixture:

$\frac{187.5+x}{750+x}=\frac{70}{100}=0.7$

Step 3: Solve for $x$.

Multiply both sides by $(750+x)$:

$187.5+x=0.7\times (750+x)$

Expand the right side:

$187.5+x=525+0.7x$

Rearrange to isolate terms with $x$ on one side:

$x-0.7x=525-187.5$

$0.3x=337.5$

$x=\frac{337.5}{0.3}=1125\text{ kg}$

Therefore, 1125 kg of tin must be added to make it 70% of the mixture.