Question 964071
the cost of pure milk is 12 rupees.


milkman adds water to 16 liters of pure milk and sells the mixture at 10 rupees per liter.


he makes a 25% profit.


how many liters of water does he add?


if he sells the milk for 10 rupees per liter and he makes a 25% profit, then the cost of the mixture to him must be 8 rupees because 8 * 1.25 = 10.


if 1 liter of milk costs 12 rupees, then x liters of milk will cost 8 rupees.


set up a ratio as shown below:


8/12 = x/1


this ratio says that 8 rupees is to 12 rupees as x liters of pure milk is to 1 liter of pure milk.


solve the ratio to get x = 8/12 = 2/3.


he needs to have 2/3 liters of pure milk in the mixture.


the rest is water.


each liter of the mixture will be 2/3 liters of pure milk plus 1/3 liters of water.


the cost to him will be 2/3 * 12 = 8 rupees plus 1/3 * 0 = 0 rupees for the water for a total cost of 8 rupees.


he sells the mixture for 10 rupees.


his profit is 2 rupees.


profit / cost = 2/8 = 25% profit.


milkman had a total of 16 liters of pure milk.


the 16 liters of pure milk is equal to 2/3 of the mixture.


16 = 2/3 * y, where y is the number of liters of the mixture.


solve for y to get y = 3/2 * 16 = 24 liters of the mixture.


he sold 24 liters of the mixture.


he added 24 - 16 = 8 liters of pure water.


24 liters of the mixture at 10 dollars per liter of the mixture is equal to 240 rupees.


his cost was 16 * 12 = 192 rupees.


his profit was 240 - 192 = 48 rupees.


his percent profit was 48 / 192 * 100 = 25%.