The acid and water in two vessels A and B are in the ratio 4 : 3 and 2 : 3. In what ratio should the liquids in both the vessles be mixed to obtain a new mixture in vessel C containing half acid and half water?

Vessel A has acid:water = 4:3, so acid concentration = 4/7 ≈ 57.14%. Vessel B has acid:water = 2:3, so acid concentration = 2/5 = 40%. To get a 50% acid mixture (half acid, half water), use the allegation method. The differences are: A is 57.14-50 = +7.14%, B is 40-50 = -10%. Taking these as 10:7.14 and simplifying gives the ratio 7:5. Therefore, mix 7 parts from A with 5 parts from B.