A mixture contains milk and water in the ratio 7:3 and another mixture of the same contains milk and water ratio 2:3. In what ratio should the mixtures be mixed in order to obtain a new mixture consisting of milk and water in the ratio 5:3? एक मिश्रण में दूध और पानी 7:3 के अनुपात में है और एक अन्य मिश्रण में दूध और पानी 2:3 के अनुपात में है। मिश्रण को किस अनुपात में मिलाना चाहिए ताकि एक ऐसा नया मिश्रण मिले जिसमें दूध और पानी 5:3 के अनुपात में है।

Let the mixtures be combined in ratio x:y. Milk from mixture 1 is (7/10)x, from mixture 2 is (2/5)y. Total milk = (7/10)x + (2/5)y. Total volume = x + y. We need milk:water = 5:3, so milk is 5/8 of total. Setting up: (7x/10 + 2y/5)/(x+y) = 5/8. Cross-multiplying: 8(7x/10 + 2y/5) = 5(x+y). Solving: 28x/10 + 16y/10 = 5x + 5y. This gives 28x + 16y = 50x + 50y, or -22x = 34y, which gives x:y = 3:1 approximately. Verification with x=3, y=1 gives milk fraction = (21/10 + 2/5)/4 = 23/40 = 0.575 = 5/8.