The amount of water that must be added to 45 litres of pure milk at \(2\displaystyle\frac{1}{2}\) litres for Rs. 120 so as to have a mixture worth Rs. 36 a litre is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 15 litres
Cost price of milk:
\( \displaystyle \frac{120}{2.5} = 48 \text{ rupees per litre} \)
Water costs nothing. By the rule of alligation with mean price 36:
\( \displaystyle \frac{\text{milk}}{\text{water}} = \frac{36 - 0}{48 - 36} = \frac{36}{12} = \frac{3}{1} \)
So for 45 litres of milk the water needed is
\( \displaystyle \frac{45}{3} = 15 \text{ litres} \)
Check: 45 litres of milk cost Rs. 2160; spread over 60 litres of mixture this is Rs. 36 a litre.