If water is mixed with milk to gain 20% by selling the mixture at cost price. Then ratio of water to milk in mixture, is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1 : 5
Let the cost price of milk be Rs. 1 per litre; water costs nothing. The mixture is sold at the cost price of milk, Rs. 1 per litre, with a gain of 20%, so the cost of 1 litre of mixture is
\( \displaystyle \text{CP} = \frac{100}{120} \times 1 = \frac{5}{6} \)
The whole cost comes from the milk, so 1 litre of mixture contains \(\frac{5}{6}\) litre of milk and \(\frac{1}{6}\) litre of water.
\( \displaystyle \text{Water} : \text{Milk} = \frac{1}{6} : \frac{5}{6} = 1 : 5 \)
Shortcut: When the mixture is sold at the cost price of milk, the gain comes only from the water, so \(\text{Water} : \text{Milk} = \text{gain}\% : 100 = 20 : 100 = 1 : 5\).