A dishonest shopkeeper buys milk at Rs 24 per litre, adds water equal to \(\frac{1}{3}\) of the quantity of milk, and sells the mixture at Rs 32 per litre. What is his gain per cent?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 77.78%
Water costs the shopkeeper nothing, so his cost is only for the milk, while he is paid for the whole mixture. Working with 1 litre of milk keeps the figures small.
Cost of 1 litre of milk \(=\) Rs 24
Water added \(\displaystyle =\frac{1}{3}\) litre, so the mixture is \(\displaystyle 1+\frac{1}{3}=\frac{4}{3}\) litres
Selling price \(\displaystyle =\frac{4}{3}\times32=\frac{128}{3}=\) Rs 42.67
Gain \(\displaystyle =\frac{128}{3}-24=\frac{56}{3}\)
Gain % \(\displaystyle =\frac{56}{3}\div24\times100=\frac{56}{72}\times100=77.78\%\)
His gain is 77.78%.