A merchant buys two items together for Rs 7,500. He sells one item at a profit of 16% and the other item at a loss of 14%. Overall he makes no profit and no loss. What is the difference between the selling prices of the two items?

Introduction / Context:
This final question is similar in structure to an earlier one: two items are bought together, one sold at profit and the other at loss, with a net result of no overall gain or loss. Here, instead of asking for a particular selling price, the problem asks for the difference between selling prices. This tests your ability to set up equations with multiple unknowns and then compute a derived quantity (difference) rather than a direct variable.

Given Data / Assumptions:

• Total cost price of the two items = Rs 7,500.
• First item is sold at 16% profit.
• Second item is sold at 14% loss.
• Net effect: no profit, no loss.
• We must find the difference between the selling prices of the two items.

Concept / Approach:
Let cost price of the profit item be x and cost price of the loss item be 7,500 - x. The corresponding selling prices are 1.16x and 0.86(7,500 - x). The condition of zero net profit implies total selling price equals total cost, so 1.16x + 0.86(7,500 - x) = 7,500. Solving this equation gives x, and thus the two selling prices. The absolute difference between these two selling prices is then our required answer.

Step-by-Step Solution:
Step 1: Let cost price of item 1 (profit item) = x.Step 2: Cost price of item 2 (loss item) = 7,500 - x.Step 3: Selling price of item 1, SP₁ = 1.16x.Step 4: Selling price of item 2, SP₂ = 0.86(7,500 - x).Step 5: No overall profit means SP₁ + SP₂ = 7,500.Step 6: So 1.16x + 0.86(7,500 - x) = 7,500.Step 7: Expand: 1.16x + 6,450 - 0.86x = 7,500 ⇒ (1.16x - 0.86x) + 6,450 = 7,500.Step 8: 0.30x = 1,050 ⇒ x = 1,050 / 0.30 = 3,500.Step 9: Then SP₁ = 1.16 * 3,500 = 4,060 and SP₂ = 0.86 * (7,500 - 3,500) = 0.86 * 4,000 = 3,440.Step 10: Difference in selling prices = |4,060 - 3,440| = Rs 620.

Verification / Alternative check:
Check that net profit is indeed zero. Total cost = 7,500. Total selling price = 4,060 + 3,440 = 7,500. Since total SP equals total CP, the merchant neither gains nor loses overall. The difference of Rs 620 is purely the result of the different profit and loss percentages applied to different cost price portions, confirming our calculation.

Why Other Options Are Wrong:
Values such as Rs 654, Rs 725 and Rs 747 would appear only if one mis-specified the profit or loss percentages, or incorrectly apportioned the total cost between the two items. They do not maintain the required condition of zero net profit when recomputing total selling price. Only Rs 620 fits all given information.

Common Pitfalls:
Some students assume equal cost prices for both items or attempt to average profit and loss percentages. Others forget that the net result being zero profit means total selling price must equal total cost. Always define variables for the unknown cost prices, correctly express selling prices in terms of those variables, and use the net profit condition to derive your equations.

Final Answer:
The difference between the selling prices of the two items is Rs. 620.