A vessel X contains 119 litres of mixture of acetic acid and water in the ratio of 10 : 7. 34 litres of mixture is taken out from vessel X and poured into a vessel Y, in which the ratio of acetic acid and water is 8 : 5. The final quantity of acetic acid in vessel Y is 26 litres more than the final quantity of acetic acid in vessel X. Find the final quantity of water in the vessel Y.

The initial mixture in vessel X totals 119 litres, meaning the 34 litres removed contains 20 litres of acetic acid and 14 litres of water. Vessel Y initially has a ratio of 8 to 5, so if its initial acid is 8x, its initial water is 5x; adding the transferred mixture makes the final acid 8x plus 20 and water 5x plus 14. Since the final acid in vessel Y (8x plus 20) is 26 litres more than the final acid in vessel X (70 minus 20, which is 50), we solve 8x plus 20 equals 76 to find x equals 7. The final quantity of water in vessel Y is 5x plus 14, which calculates to 5 times 7 plus 14, resulting in 49 litres.

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