Question

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains $20\%.$ The percentage of water in the mixture is

• A. $4\%$
• B. $16.66\%$
• C. $20\%$
• D. $25\%$

Answer 1

The correct option is C $20\%$

If a trader professes to sell his goods at cost price but uses false weights, then

Gain$\%=\frac{Error}{Truevalue-Error}\times 100\%$

Here gain$=25\%$

Here error$=$ quantity of water he mixes in the milk$=x$

Here the true value$=$true quantity of milk$=T$

So the formula becomes $25=\frac{x}{T-x}\times 100$

$\Rightarrow 1=\frac{x}{T-x}\times 4$

$\Rightarrow T-x=4x$

$\Rightarrow T=5x$

Percentage of water in the mixture$=\frac{x}{T}\times 100=\frac{x}{5x}\times 100=20\%$