In what ratio must water be mixed with milk to gain 15% by selling the mixture at cost price? 

Correct option is D

Solution:

Let the cost price of 1 unit of milk be ₹1.

When the mixture is sold at the cost price, it means the selling price of the mixture is equal to the cost price of the milk.

Let the quantity of milk be M units and the quantity of water be W units.

Total Cost of the mixture = Cost of Milk = M × ₹1 = ₹M

Total Selling Price of the mixture = (M+W) × ₹1 = ₹(M + W) (since sold at the cost price of milk)

Profit = Selling Price - Cost Price

Profit = (M + W) - M = W

Given Profit Percentage = 15%

Profit Percentage =$$\frac{\text{Profit}}{\text{Cost Price}} \times 100$$​​

15 =$$\frac{W}{M} \times 100$$​

$$\frac WM=\frac{15}{100}=\frac 3{20}$$​

So, the ratio of Water to Milk (Water : Milk) is 3 : 20.