Profit and Loss – Successive resales of land: A piece of land passes through three hands. Overall, its price rises by 65%. If the first seller earns a 20% profit and the second seller earns a 25% profit, what is the profit percentage earned by the third seller?

Introduction / Context:
When a commodity is resold multiple times, overall percentage change equals the compounded effect of individual stage changes. If two stage gains are known and the overall gain is given, we can back out the missing stage gain by working with a convenient base, such as an initial price of 100 units.

Given Data / Assumptions:

• Overall rise = 65%
• First seller’s profit = 20%
• Second seller’s profit = 25%

Concept / Approach:
Assume original price = 100. After 20% gain it becomes 120. After 25% gain it becomes 120 * 1.25 = 150. To achieve a total 65% rise, final price must be 165. The third seller’s profit is the percentage rise from 150 to 165.

Step-by-Step Solution:
Start price = 100After 1st sale: 100 * 1.20 = 120After 2nd sale: 120 * 1.25 = 150Final price (overall +65%) = 165Third seller’s gain% = (165 − 150) / 150 * 100 = 10%

Verification / Alternative check:
Multiply stage factors: 1.20 * 1.25 * 1.10 = 1.65, which exactly matches the overall rise of 65%.

Why Other Options Are Wrong:
20% and 25% misread the remaining gap. 55% is the net total, not the third-stage gain. 15% overstates the final step.

Common Pitfalls:
Adding 20+25 and subtracting from 65; percentage changes compose multiplicatively, not additively.

Final Answer:
10%