In what ratio milk and water be mixed so that on selling the mixture at the cost price there would be a profit of 10%? दूध और पानी को किस अनुपात में मिलाकर बेचा जाय कि प्राप्त मिश्रण को क्रय मूल्य में बेचने पर 10% का लाभ प्राप्त हो ?

Let milk be m parts and water be w parts. Cost of milk per unit = 1, cost of water = 0. Total cost = m, total quantity = m + w. CP of mixture = m/(m+w). For 10% profit selling at CP, we need: SP = CP × 1.1 = cost price. This means the actual CP must be such that when sold at that price, we make 10% profit. If we sell at the milk's cost price, we need the mixture to cost 1/1.1 times the milk price. So m/(m+w) = 1/1.1 = 10/11. Cross-multiplying: 11m = 10m + 10w, so m = 10w. Therefore, ratio milk:water = 10:1.