Two mixtures have copper and zinc in the ratio of 2:1 and 4:1 respectively. In what ratio these two mixtures have to be mixed so that the ratio of copper and zinc in the final mixture is 3:1?

Let the mixtures be combined in ratio x:y. Mixture 1 has copper as 2/3 of its content, zinc as 1/3. Mixture 2 has copper as 4/5, zinc as 1/5. For final ratio 3:1: [(2/3)x + (4/5)y] / [(1/3)x + (1/5)y] = 3/1. Solving: (2/3)x + (4/5)y = x + (3/5)y, giving (1/5)y = (1/3)x, so x:y = 3:5. This gives copper:zinc = [(2/3)(3) + (4/5)(5)] / [(1/3)(3) + (1/5)(5)] = (2+4)/(1+1) = 6/2 = 3/1 ✓