A dishonest milkman professes to sell his milk at cost price but he mixes it wit

Question

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:

Options:

A . 4%

B . \(6\frac{1}{4}\)%

C . 20%

D . 25%

Answer: Option C

Let C.P. of 1 litre milk be Re. 1

Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.

C.P. of 1 litre mixture = Re. \(\left(\frac{100}{125}\times1\right)=\frac{4}{5}\)

By the rule of alligation, we have:

C.P. of 1 litre of milk = Rs.1

C.P. of 1 litre of water = 0

So, Ratio of milk to water = \(\frac{4}{5}:\frac{1}{5}=4:1.\)

Hence, percentage of water in the mixture = \(\left(\frac{1}{5}\times100\right)\) % = 20%

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