Question

A milkman purchases milk at Rs $20/$litre and mixes $4$ litres of water in it. By selling the resultant mixture at the rate of Rs $20/$litre, he earns a profit of $40\%$. The percentage of milk in the mixture he had with him to sell was

• A. $33\%$
• B. $71.43\%$
• C. $28.57\%$
• D. $57\%$

Answer 1

The correct option is B $71.43\%$

Let the milkman purchased $x$ litres of milk.
After mixing $4$ litres of water, he has $(x+4)$ litres mixture to sell.
Profit $\%=\frac{S.P.-C.P.}{C.P.}\times 100$
where $C.P.=$ cost price and $S.P.=$ selling price
Now, given that profit $=40\%$
$\Rightarrow \frac{40}{100}=\frac{20(x+4)-20x}{20x}$
$\Rightarrow 4=\frac{80}{2x}$
$\Rightarrow x=10$
Milkman sold $x+4=10+4=14$ litres mixture
Milk $\%$ in the mixture $=\frac{10}{14}\times 100=71.43\%$