In what ratio, water must be added to dilute honey costing Rs. 320 per liter so that the resulted syrup would be worth Rs. 280 per liter?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1 : 7
Water costs Rs. 0 per litre. By the rule of alligation, with mean price 280:
\( \displaystyle \frac{\text{Water}}{\text{Honey}} = \frac{\text{Price of honey} - \text{Mean price}}{\text{Mean price} - \text{Price of water}} \)
\( \displaystyle \frac{\text{Water}}{\text{Honey}} = \frac{320 - 280}{280 - 0} = \frac{40}{280} = \frac{1}{7} \)
So water must be added to honey in the ratio 1 : 7.
Check: 7 litres of honey cost Rs. 2240; with 1 litre of water the 8 litres are worth Rs. 2240 ÷ 8 = Rs. 280 per litre.