Question 106

A milk vendor sells 10 litres of milk from a can containing 40 litres of pure milk to the 1st customer. He then adds 10 litres of water to the milk can. He again sells 10 litres of mixture to the 2nd customer and then adds 10 litres of water to the can. Again he sells 10 litres of mixture to the 3rd customer and then adds 10 litres of water to the can and so on. What amount of pure milk will the 5th customer receive?

Solution

The amount of pure milk received by 5th customer = amount of pure milk after 4 replacements - amount of milk after 5 replacements

Formula for amount of milk after n replacements is : 40 $$(1 - \frac{10}{40})^{n}$$

Amount of milk received by 5th customer = 40 $$(1 - \frac{10}{40})^{4}$$ - 40 $$(1 - \frac{10}{40})^{5}$$

=> 40 * $$(\frac{3}{4})^{4} (1 - \frac{3}{4})$$

=> $$\frac{405}{128}$$ lts.

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