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

• A. $4$%
• B. $6\frac{1}{4}$%
• C. $20$%
• D. $25$%

Answer 1

The correct option is C $20$%

According to the question,

Let's assume milkman has $100$ liter of milk, If he added $x$ liter of water, the percentage of water in the mixture$=\frac{x}{(100+x)}\times 100$

The milk gain $25$%, he must have added $25$ liter water in $100$ liter of milk. Then the percentage of water in the mixture$=\frac{25}{(100+25)}\times 100=20\%$

In the new mixture, If the milk is $80$% then $80$% of total mixture should be $100$ liter

$(100+x)\times \frac{80}{100}=100$

$8x=200$

$x=25$

Then, the percentage of water in the mixture $=\frac{25}{(100+25)}\times 100=20\%$