Vessel I filled up to its brim by milk is completely emptied into two vessels II and III. The ratio of milk in vessel I and II is 5 : 3, respectively. If 48 litres is now transferred from vessel II to III, then the quantity of milk in vessel III becomes twice the quantity of milk in vessel II. What was the initial quantity (in litres) of milk in vessel I?

Let the total initial quantity of milk in vessel I be 5x, making the quantity poured into vessel II equal to 3x. After transferring 48 liters from vessel II, the remaining quantity in vessel II is (3x minus 48) liters, which is half of the new quantity in vessel III, so vessel III now contains 2 multiplied by (3x minus 48) liters. Since the total milk distributed between vessel II and vessel III remains 5x, the equation is 3 multiplied by (3x minus 48) equals 5x; solving this gives 9x minus 144 equals 5x, resulting in x equals 36. The initial quantity of milk in vessel I was 5x, so the total is 180 liters.

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