Two vessels A and B contain sprit and water mixed in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C, containing sprit and water in the ratio 8 : 5?

Using allegation: Vessel A has 5/7 spirit, B has 7/13 spirit, target is 8/13 spirit. Ratio = |(8/13 - 7/13)| : |(5/7 - 8/13)| = (1/13) : |(65-56)/91| = (1/13) : (9/91) = 7:9. Verifying: 7 parts of A (35/7=5 units spirit, 14/7=2 units water) + 9 parts of B (63/13≈4.85 spirit, 54/13≈4.15 water) gives total 9.85:6.15 ≈ 8:5.