A merchant offers a discount of 25% on the list price of an item and then incurs a loss of 5%. What percentage profit or loss will the merchant make if instead the item is sold at a discount of only 10% on the same list price?

Introduction / Context:
This question combines discount and profit or loss concepts. The key idea is that discount is applied on the list (marked) price, while profit or loss is always calculated on the cost price. You are given one selling scenario that leads to loss and are asked to find the percentage profit or loss in a different discount scenario using the same list price. This type of question appears frequently in aptitude tests to check conceptual clarity on pricing structures.

Given Data / Assumptions:

• Let the list price be L.
• First case: discount = 25%, so selling price SP1 = 0.75L.
• Under SP1, the merchant has a loss of 5%.
• Second case: discount = 10%, so selling price SP2 = 0.90L.
• We must find the profit or loss percentage in the second case.
• No taxes, extra costs, or hidden charges are mentioned.

Concept / Approach:
The steps are:

• Use the first scenario to relate cost price (CP) and list price L.
• Loss of 5% means SP1 = 0.95 * CP.
• Equate 0.75L = 0.95 * CP to find CP in terms of L.
• Use this CP and SP2 = 0.90L to compute profit percentage in the second scenario.

The key formula is profit percentage = ((SP - CP) / CP) * 100.

Step-by-Step Solution:
Step 1: From first case, SP1 = 0.75L. Step 2: Loss of 5% means SP1 = 0.95 * CP. Step 3: So 0.75L = 0.95 * CP, hence CP = 0.75L / 0.95. Step 4: In the second case, SP2 = 0.90L (10% discount on list price). Step 5: Profit percentage in second case = ((SP2 - CP) / CP) * 100. Step 6: Substitute CP: SP2 - CP = 0.90L - (0.75L / 0.95). Step 7: Compute CP in fraction form: CP = (75 / 95)L = (15 / 19)L. Step 8: SP2 = 0.90L = (9 / 10)L. Step 9: Profit fraction = ((9 / 10)L - (15 / 19)L) / ((15 / 19)L). Step 10: Simplify numerator: (9 / 10 - 15 / 19)L = ((171 - 150) / 190)L = (21 / 190)L. Step 11: Divide by CP: (21 / 190)L / ((15 / 19)L) = (21 / 190) * (19 / 15) = 1 / 7. Step 12: Profit percentage = (1 / 7) * 100 ≈ 14% profit.

Verification / Alternative check:
Take a convenient value for L, for example L = Rs 190. Then:

• SP1 = 0.75 * 190 = Rs 142.50.
• Since SP1 is at 5% loss, CP = SP1 / 0.95 = 142.50 / 0.95 = Rs 150.
• In the second case, SP2 = 0.90 * 190 = Rs 171.
• Profit = SP2 - CP = 171 - 150 = Rs 21.
• Profit percentage = 21 / 150 * 100 = 14%.

This numerical check fully confirms the symbolic calculation.

Why Other Options Are Wrong:
5.5 percent loss: This would imply SP2 is less than CP, which contradicts our calculation that SP2 is higher.
50 percent profit: This would require much larger difference between SP2 and CP than observed.
26 percent loss: Also inconsistent because SP2 is clearly above CP once numbers are plugged in.
Therefore, these values do not satisfy the relationship between list price, discounts, and cost price derived from the first scenario.

Common Pitfalls:
A frequent mistake is to treat discount percentage and loss percentage as directly comparable and to attempt adding or subtracting them without considering bases. Another error is to assume CP equals the list price, which is not stated. Some students may also incorrectly use SP1 as CP for the second case. The correct approach is always to find CP from one scenario, then use that CP to analyze any new selling arrangement.

Final Answer:
If the item is sold at a 10% discount on the list price, the merchant makes a 14 percent profit.