Srinivas bought 10 cycles for Rs 1,750 each. He sold 4 cycles for Rs 8,400 in total and 3 cycles for Rs 1,900 each. At what price should he sell each of the remaining cycles so that his average profit is Rs 320 per cycle?

Introduction / Context:
This is a profit and loss question involving multiple items with different selling prices. Srinivas buys several cycles at the same cost price but sells them in different lots at different selling prices. You are asked to find the selling price of the remaining cycles so that the overall average profit per cycle reaches a specified amount. This tests your ability to work with total cost, total revenue and average profit concepts in arithmetic.

Given Data / Assumptions:

• Srinivas bought 10 cycles at Rs 1,750 each.
• He sold 4 cycles for Rs 8,400 in total.
• He sold 3 cycles for Rs 1,900 each.
• He wants an average profit of Rs 320 per cycle on all 10 cycles.
• We must find the selling price per cycle for the remaining 3 cycles.

Concept / Approach:
The key idea is to work with totals. First find the total cost of all cycles. Then compute the total revenue needed to achieve the desired average profit. Subtract the revenue already earned from the sold cycles to find how much more revenue is needed from the remaining cycles. Finally, divide this required revenue by the number of remaining cycles to get the selling price per remaining cycle. This approach avoids mixing up individual profits and focuses on overall totals, which is easier and more reliable.

Step-by-Step Solution:
Step 1: Compute the total cost price. Each cycle costs Rs 1,750 and there are 10 cycles, so total cost = 10 * 1750 = Rs 17,500. Step 2: He wants an average profit of Rs 320 per cycle on 10 cycles. Total profit required = 10 * 320 = Rs 3,200. Step 3: Total revenue required to achieve this profit is total cost + total profit = 17,500 + 3,200 = Rs 20,700. Step 4: Now compute the revenue already earned. He sold 4 cycles for a total of Rs 8,400. Step 5: He sold another 3 cycles at Rs 1,900 each, giving 3 * 1,900 = Rs 5,700. Step 6: Total revenue from the 7 cycles sold = 8,400 + 5,700 = Rs 14,100. Step 7: Remaining revenue needed = 20,700 − 14,100 = Rs 6,600. Step 8: There are 3 cycles left, so each must be sold at 6,600 / 3 = Rs 2,200.

Verification / Alternative check:
Verify the final profit. If each of the remaining 3 cycles is sold at Rs 2,200, revenue from these 3 cycles is Rs 6,600. Add this to the previous revenue of Rs 14,100 to get total revenue of Rs 20,700. Subtract total cost of Rs 17,500: total profit = 20,700 − 17,500 = Rs 3,200. Divide by 10 cycles to get average profit = 3,200 / 10 = Rs 320 per cycle, which matches the requirement. This confirms that the selling price of Rs 2,200 per remaining cycle is correct.

Why Other Options Are Wrong:
Option Rs. 1580 and Rs. 1785: These are too low and would reduce the overall average profit below Rs 320 per cycle.
Option Rs. 1950 and Rs. 2100: These would give some profit, but when you calculate total revenue and total profit, the average profit per cycle will be less than Rs 320.

Common Pitfalls:
A common mistake is to try to compute profit separately for each batch and then average those profits, which does not always give the correct overall average profit. Another error is to forget to multiply the profit per cycle by the total number of cycles when calculating the required total profit. Always work with total cost, total required profit, and total revenue to avoid confusion. Then distribute the remaining required revenue evenly across the remaining items.

Final Answer:
Srinivas should sell each of the remaining cycles for Rs 2,200 to earn an average profit of Rs 320 per cycle.