A vendor sells a coconut at Rs 24 and incurs a loss of 20%. If instead he sells a coconut at Rs 36, what will be his profit percentage?

Introduction / Context:
This is a two stage profit and loss question. The vendor first sells a coconut at a loss, which allows us to reconstruct the cost price. Later, he sells at a higher price, and we must calculate the profit percentage. This type of question checks your ability to move from one selling situation to another by correctly identifying and reusing the cost price as a fixed reference point.

Given Data / Assumptions:

• When the coconut is sold at Rs 24, there is a loss of 20%.
• When it is sold at Rs 36, we must find the profit percentage.
• Let CP be the cost price of one coconut.
• Loss and profit percentages are calculated on CP.

Concept / Approach:
Loss of 20% means the selling price is 80% of the cost price. Using this relation, we compute cost price from the first scenario. With the cost price known, we then compute the profit when the coconut is sold at the second selling price by the formula profit% = (SP - CP) / CP * 100. Identifying that CP is the same for both transactions is essential for the correct solution.

Step-by-Step Solution:
Step 1: Let cost price be CP.Step 2: At SP = 24, loss = 20%, so SP = 80% of CP = 0.80 * CP.Step 3: Thus 0.80 * CP = 24.Step 4: CP = 24 / 0.80 = 30.Step 5: Now consider SP2 = 36.Step 6: Profit when selling at 36 = SP2 - CP = 36 - 30 = 6.Step 7: Profit percentage = (6 / 30) * 100 = 20%.Step 8: Therefore the vendor earns a 20% profit when selling at Rs 36.

Verification / Alternative check:
We can verify reasoning by checking both cases around CP = 30. At SP = 24, the loss is 6 on 30, that is 6 / 30 * 100 = 20% loss, which matches the given. At SP = 36, the profit is also 6 on 30, that is 20% profit. This symmetry around the cost price confirms that the cost price is exactly midway between the two selling prices and that the profit percentage at Rs 36 is indeed 20%.

Why Other Options Are Wrong:
Option A (10), option C (30), and option D (40) do not match the computed profit percentage. A 10% profit would imply a cost price different from Rs 30, and 30% or 40% would require larger differences between SP and CP. Only option B, 20, correctly reflects the profit percentage when the cost price is Rs 30 and the selling price is Rs 36.

Common Pitfalls:
Some students incorrectly think that if 24 yields a 20% loss, then 36 might yield a 20% gain without checking the arithmetic. Others confuse which value is cost price and which is selling price when setting up the first equation. It is important to first solve precisely for cost price using the loss condition before jumping to conclusions about profit in the second case.

Final Answer:
When he sells a coconut at Rs 36, the vendor makes a 20% profit.