Pure milk costs Rs. 80 per litre. A milkman adds water to 24 litres of pure milk and sells the mixture at Rs. 60 per litre without extra gain or loss. How many litres of water does he add?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8
Water costs nothing, so the cost of the mixture equals the cost of the milk:
\( \displaystyle \text{cost of milk}=24\times 80=\text{Rs. }1920 \)
With no gain or loss, the selling price of the whole mixture is also Rs. 1920:
\( \displaystyle \text{volume of mixture}=\frac{1920}{60}=32\ \text{litres} \)
\( \displaystyle \text{water added}=32-24=8\ \text{litres} \)
Shortcut: By alligation (milk Rs. 80, water Rs. 0, mean Rs. 60): milk : water = (60 − 0) : (80 − 60) = 3 : 1, so water = \( \frac{24}{3}=8 \) litres.