A shopkeeper purchased 10 kg of Basmati rice at the rate of
Rs. 50 per kg and 15 kg of ordinary rice at the rate of Rs. 20 per
kg. He mixed the two varieties of the rice and sold it for a gain
of 25%. What was his sale price (Rs/kg)?

The correct option is Rs 40 per kg.

Let us break down the solution step-by-step to understand how we arrive at this sale price.

Step 1: Calculate the total cost price (CP) of the mixture
The shopkeeper bought two varieties of rice:
1. 10 kg of Basmati rice at Rs. 50 per kg:
Cost of Basmati rice = $10\times 50=500$ Rs.
2. 15 kg of ordinary rice at Rs. 20 per kg:
Cost of ordinary rice = $15\times 20=300$ Rs.

Total cost of the mixture = Cost of Basmati rice + Cost of ordinary rice
Total Cost Price (CP) = $500+300=800$ Rs.

Step 2: Calculate the total quantity of the mixture
Total quantity = 10 kg + 15 kg = 25 kg.

Step 3: Calculate the total selling price (SP) for a 25% gain
The shopkeeper wants to make a 25% profit on his total investment (CP).
Total Selling Price (SP) = CP + 25% of CP
Total Selling Price (SP) = $800\times \left(1+\frac{25}{100}\right)=800\times 1.25=1000$ Rs.

Step 4: Calculate the selling price per kg of the mixture
To find the rate at which the mixture should be sold, we divide the total selling price by the total quantity:
Selling Price per kg = Total Selling Price / Total Quantity
Selling Price per kg = $\frac{1000}{25}=40$ Rs/kg.

Therefore, the sale price of the mixed rice was Rs. 40 per kg.