Alloy A has gold and copper in the ratio 3 : 2; alloy B has them in the ratio 1 : 4. In what ratio must A and B be melted together to get an alloy with equal amounts of gold and copper?

Explanation

1. 01

   The share of gold is $\frac{3}{5}$ in A, $\frac{1}{5}$ in B and $\frac{1}{2}$ in the mixture.

2. 02

   A : B $= \left(\frac{1}{2} - \frac{1}{5}\right) : \left(\frac{3}{5} - \frac{1}{2}\right) = \frac{3}{10} : \frac{1}{10} = 3 : 1$.