Given: Ratio of milk and water in two vessels = 9 : 5 and 10 : 7 Concept used: (x1 + x2)/(y1 + y2) = a/b x1, x2 = quantities of 1st type item y1, y2 = quantities of 2nd type item a, b = final ratio Calculation: Let milk and water in 1st vessel = 9x and 5x ⇒ Milk and water in 2nd vessel = 10y : 7y According to the question, 9x + 5x = 10y + 7y 14x = 17y ⇒ x/y = 17/14 Milk and water in 1st vessel = 9 × 17 and 5 × 17 ⇒ 153L and 85L Milk and water in 2nd vessel = 10 × 14 and 7 × 14 ⇒ 140L and 98L Total in milk and water in 3rd vessel = (153 + 140) and (85 + 98) ⇒ 293 and 183 ⇒ Ratio of milk and water = 293 : 183 ∴ The new ratio of water and milk in the third vessel is 183 : 293