An alloy of gold and silver contains 20% gold what mass of the alloy and what mass of pure gold you need

An alloy of gold and silver contains 20% gold what mass of the alloy and what mass of pure gold you need to take to get 80 kilograms of a new alloy containing 50% gold.

If 50% of the new alloy is to contain gold, then the remaining 50% is impurities. 50% of 80 kg is 80 * 0.5 = 40 kg.

In the original alloy, impurities are 100% – 20% = 80%. Let’s find 80% of which number is 40 kg:

40: 80 * 100 = 50 (kg).

This means that if you take 50 kg of the initial mixture, then they will contain 40 kg of impurities and 10 kg of gold. This means that you need to take another 40 – 10 = 30 kg of gold.

Answer: you need to take 50 kg of alloy and 30 kg of gold.