Ajay mixes 15 kg of dal bought at Rs. 14.50 per kg with 10 kg of dal bought at Rs. 13 per kg and sells the entire 25 kg mixture at Rs. 15 per kg; what is his total gain in rupees on this transaction?

Introduction / Context:
This mixture and profit problem involves combining two types of dal purchased at different rates and then selling the mixture at a single uniform price. The question requires calculation of the total profit in rupees, not just the profit percentage. Such problems test the ability to compute weighted average cost and compare it with the realized selling price for the whole batch.

Given Data / Assumptions:

• Ajay buys 15 kg of dal at Rs. 14.50 per kg.
• He buys another 10 kg of dal at Rs. 13 per kg.
• Total mixture quantity = 15 + 10 = 25 kg.
• He sells the mixture at Rs. 15 per kg.
• No wastage or extra cost is mentioned.
• We need to find total gain in rupees.

Concept / Approach:
The method is to compute the total cost of both types of dal, then compute the total revenue from selling the whole mixture. The difference between total revenue and total cost is the profit. It is important to work with the total amounts first, and only then derive any average if needed. Here the question explicitly asks for the profit in rupees, so we will stop at that value after the calculations.

Step-by-Step Solution:
Step 1: Cost of first type of dal = 15 kg * Rs. 14.50 per kg.Step 2: Compute 15 * 14.50 = 15 * 14 + 15 * 0.5 = 210 + 7.5 = Rs. 217.50.Step 3: Cost of second type of dal = 10 kg * Rs. 13 per kg = Rs. 130.Step 4: Total cost price of mixture = 217.50 + 130 = Rs. 347.50.Step 5: Total quantity of mixture = 15 + 10 = 25 kg.Step 6: Selling price per kg of mixture = Rs. 15.Step 7: Total selling price = 25 * 15 = Rs. 375.Step 8: Profit (gain) = Total selling price minus Total cost price.Step 9: Profit = 375 - 347.50 = Rs. 27.50.

Verification / Alternative check:
We can compute the average cost price per kg and then compare it with the selling price per kg. Average cost per kg = Total cost / Total quantity = 347.50 / 25 = 13.90. Selling price per kg = 15. Profit per kg = 15 - 13.90 = Rs. 1.10. Multiply this by total 25 kg to get total profit = 1.10 * 25 = Rs. 27.50. This confirms that both methods give the same profit value, so our calculation is correct.

Why Other Options Are Wrong:

• Rs. 1.10: This is the profit per kg, not the total profit on 25 kg.
• Rs. 11 and Rs. 16.50: These represent possible partial profits if fewer kilograms were sold, but they do not match the full transaction.

Common Pitfalls:

• Adding the two price rates directly and averaging without weighting according to quantities, which leads to an incorrect average cost.
• Confusing profit per kg with total profit, especially when one notices Rs. 1.10 as the per kg margin.
• Rounding off intermediate values too early instead of keeping exact figures like Rs. 217.50.

Final Answer:
Ajay gains a total of Rs. 27.50 from selling the mixed dal at Rs. 15 per kg.