Correct Answer: 10 kg

Solution : Given:
Cost price of wheat = Rs. 30 per kg
Selling price of 8 kg = Rs. $x$ per kg
The selling price of the remaining wheat = Rs. 45 per kg
Overall profit percentage = 10%
Total cost price = CP = Rs. $30 \times x = 30x$
Profit must be 10%
So, SP = $30x \times \frac{110}{100} = 33x$
For the first 8 kg of wheat, the selling price is Rs. $x$ per kg.
Selling price of 8 kg = $8 \times x = 8x$
For the remaining wheat, the selling price is Rs. 45 per kg.
Remaining quantity = $(x - 8)$ kg
According to the question
⇒ $33x = 8x + (x - 8)45$
⇒ $33x = 8x + 45x - 8 \times 45$
⇒ $x = 18$ kg
Quantity of wheat sold at Rs. 45 per kg = $(x - 8) = 18 - 8 = 10$ kg
Therefore, Ritika sold 10 kg of wheat at Rs. 45 per kg.
Hence, the correct answer is 10 kg.