Alloy P has copper and zinc in the ratio $3 : 1$; alloy Q has them in the ratio $1 : 3$. In what ratio must P and Q be melted together to get an alloy with copper and zinc in the ratio $5 : 3$?

Explanation

1. 01

   Copper fraction: P = $\frac{3}{4} = 75\%$, Q = $\frac{1}{4} = 25\%$, target = $\frac{5}{8} = 62.5\%$.

2. 02

   $P : Q = (62.5 - 25) : (75 - 62.5) = 37.5 : 12.5$.

3. 03

   = $3 : 1$.