Question 964071: Pure milk costs Rs. 12 per litre. A milkman add some water to 16 litres of pure milk and sells the mixture at
Rs. 10 per litre by making 25% profit. How many litres of water does he added?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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%.
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