How many litres of a 12 litre mixture containing milk and water in the ratio of 2 : 3 be replaced with pure milk so that the resultant mixture contains milk and water in equal proportion? 2 : 3 के अनुपात में दूध और पानी वाले 12 लीटर मिश्रण में से कितने लीटर को शुद्ध दूध से बदल दिया जाए ताकि परिणामी मिश्रण में दूध और पानी समान अनुपात में हो?

Initial mixture has milk:water = 2:3 in 12L, so milk = (2/5)×12 = 4.8L and water = 7.2L. If x litres is removed and replaced with pure milk, milk becomes 4.8 - (2/5)x + x = 4.8 + (3/5)x, and water becomes 7.2 - (3/5)x. For equal proportions: 4.8 + 0.6x = 7.2 - 0.6x, giving 1.2x = 2.4, so x = 2L. The key is maintaining concentration when removing mixture.