How many kilograms of rice costing Rs.60 per kg must be mixed with 24 kg of rice costing Rs.42 per kg so that there may be a gain of 12% by selling the mixture at Rs.56 per kg?

Question

Accepted Answer

**Solution:**

1. Given:
   - Selling price (SP) = Rs. 56 per kg
   - Gain = 12% of cost price (CP)
   - Weight of rice costing Rs. 42 per kg = 24 kg
   - Weight of rice costing Rs. 60 per kg = ?

2. Calculate the cost price of the new mixture:
   - Since gain is 12%, SP = 112% of CP
   - Therefore, CP = $ \frac{SP}{1.12} = \frac{56}{1.12} = 50 $ Rs. per kg

3. Use alligation method to find the ratio of quantities:
   - Difference between cost price of expensive rice and mixture:
     $ 60 - 50 = 10 $
   - Difference between cost price of cheaper rice and mixture:
     $ 50 - 42 = 8 $
   - Ratio of quantities (cheaper : expensive) = 10 : 8 = 5 : 4

4. Given weight of cheaper rice = 24 kg, calculate weight of expensive rice:
   $$
   \text{Weight of expensive rice} = \frac{24 \times 4}{5} = 19.2 \text{ kg}
   $$

**Answer:** 19.2 kg

Answer

Answer

Answer