While selling a watch, a shopkeeper gives a discount of 5 percent on the marked price, and if instead he gives a discount of 7 percent he earns 15 rupees less profit. What is the marked price of the watch?

Introduction / Context:
This problem tests your understanding of how discounts affect selling price and profit for a fixed marked price. It is a typical percentage question where you must relate two different discount scenarios using a single unknown marked price and interpret a given difference in profit.

Given Data / Assumptions:
- Marked price of the watch is unknown; let it be M rupees.
- In the first case, discount = 5 percent, so selling price is 95 percent of M.
- In the second case, discount = 7 percent, so selling price is 93 percent of M.
- Profit in the second case is 15 rupees less than in the first case.
- Cost price is the same in both cases.

Concept / Approach:
The cost price does not change between scenarios, so the change in profit equals the change in selling price. Therefore the difference between the two selling prices is 15 rupees. We express both selling prices in terms of the marked price M, form an equation for their difference, and solve for M. No explicit cost price value is required because it cancels out.

Step-by-Step Solution:
Step 1: First selling price with 5 percent discount: SP1 = 95 percent of M = 0.95 * M.Step 2: Second selling price with 7 percent discount: SP2 = 93 percent of M = 0.93 * M.Step 3: Given that the profit decreases by 15 rupees when the discount goes from 5 percent to 7 percent, the selling price must also decrease by 15 rupees.Step 4: So, SP1 - SP2 = 15.Step 5: Substitute 0.95 * M - 0.93 * M = 15.Step 6: This simplifies to 0.02 * M = 15.Step 7: Therefore M = 15 / 0.02 = 750.

Verification / Alternative check:
Check quickly by computing selling prices. When M = 750, SP1 = 95 percent of 750 = 0.95 * 750 = 712.5. SP2 = 93 percent of 750 = 0.93 * 750 = 697.5. The difference SP1 - SP2 = 712.5 - 697.5 = 15, which matches the given decrease in profit, confirming that the marked price is correct.

Why Other Options Are Wrong:
- 697.5: This equals the lower selling price, not the marked price.
- 712.5: This equals the higher selling price, not the marked price.
- None of the these: This is incorrect because option 750 is a valid and consistent marked price as shown by the calculations.

Common Pitfalls:
Students sometimes try to involve the cost price directly, which complicates the problem unnecessarily. The essential idea is that profit changes by exactly the same amount as the selling price when the cost price is constant. Another mistake is to treat the 2 percent difference between 5 percent and 7 percent discounts as 2 rupees instead of expressing it as 0.02 times the marked price. Always convert percentage changes into expressions involving the unknown marked price first.

Final Answer:
The marked price of the watch is 750 rupees.