Alloy A has copper and zinc in the ratio 4 : 1 and alloy B has them in the ratio 1 : 3. In what ratio must A and B be melted together so that the new alloy has copper and zinc in the ratio 3 : 2?

Copper is 4/5 = 0.80 of A, 1/4 = 0.25 of B and must be 3/5 = 0.60 of the mixture. By alligation, A : B = (0.60 − 0.25) : (0.80 − 0.60) = 0.35 : 0.20 = 7 : 4. Check with 7 kg + 4 kg: copper 5.6 + 1 = 6.6, zinc 1.4 + 3 = 4.4, and 6.6 : 4.4 = 3 : 2. Writing the two differences the other way round gives 4 : 7, which would put more of the copper-poor alloy in and miss the target.