In what ratio should a shopkeeper mix two types of rice, one costing Rs. 20 per kg and another costing Rs. 40 per kg to get a rice variety costing Rs. 28 per kg?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3 : 2
By the rule of alligation,
\( \displaystyle \frac{\text{Quantity of cheaper}}{\text{Quantity of dearer}} = \frac{\text{Dearer price} - \text{Mean price}}{\text{Mean price} - \text{Cheaper price}} \)
\( \displaystyle = \frac{40 - 28}{28 - 20} = \frac{12}{8} = \frac{3}{2} \)
So the Rs. 20 rice and the Rs. 40 rice are mixed in the ratio 3 : 2.
Check: 3 kg at Rs. 20 and 2 kg at Rs. 40 cost Rs. 140 for 5 kg, that is, Rs. 28 per kg.