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Question

A dishonest milkman a buys $$100$$ liters of milk from another dishonest milkman $$B$$  for onward distribution. He retains $$10$$ liter of milk for personal use, adds water to make up the shortfall and sells the mixture at Rs. $$15$$ /liter, there by making a profit of Rs. $$2.75$$ /liter on the quantity sold. If $$B$$ had already diluted the milk with water in the ratio of milk : water $$9 : 1$$ and he makes a profit of Rs. $$1$$, the price per liter of pure milk purchased by $$B$$ is closest to?


Solution

$$A$$ taken milk from $$B$$  $$= 100 $$ liters
B has milk and water in $$9 : 1$$ ratio i.e. $$B$$ sold $$90$$ liters milk and $$10$$ liters water to $$A$$ instead of $$100$$ liters milk.
A retain milk $$= 10$$ liters ($$9$$ liters milk and $$1$$ liters water)
Now, $$A$$ has $$90$$ liters milk ($$81$$ liters milk and $$9$$ liters water) to sell and he has to add $$10$$ liters more water to make milk $$100$$ liters ($$81$$ milk $$+$$ $$19$$ water )
$$B$$ sells $$15$$ per/L with Rs. $$2.75$$ profit.
So, cost price of $$A$$ $$= 15 - 2.75 =$$ Rs. $$12.25$$
Cost price of $$A$$ for pure milk $$(90)$$ L $$=\dfrac {100\times 12.25}{90}=$$ Rs. $$13.61$$ per liter.

Mathematics

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