Question

The percentage of pure 24 carat gold present in a necklace weighing 4.5 kg is 25%. The ornament is melted to make a new anklet. How much amount at 24 carat gold (approximate) should be added to it so that its percentage in the new anklet is 30?

Answer 1

The percentage of pure 24 carat gold in the necklace weighing 4.5 kg is 25%.

Now that old ornament is melted to form a new one. New anklet should have 30% of gold in it.

The original weight was 4.5 kg

25% of 4.5 kg is:

$25\% \times 4.5=0.25\times 4.5=1.125$

So the original ornament had 1.125 kg of gold. Now, we need to figure out how much gold we should add more to have new percentage about 30.

So we already had 1.125 kg of gold and 3.375 kg of other material so we need to find out how much 3.375 kg of other material to be used.

$\frac{3.375}{(1.125+x)}=\frac{70}{30}$

$3(3.375)=7(1.125+x)$

Solving for 'x' we get:

$10.125=7.875+7x$

$x=\frac{10.125-7.875}{7} =0.321$

Therefore, 0.321 kg of gold must be added in the anklet so that its percentage is 30.