Sreya buys a plot for Rs. 6,00,000. She sells half of the plot at a profit of 10% and the remaining half at a profit of 15%. What is her overall profit percentage on the entire investment?

Introduction / Context:
Real estate profit problems often involve selling different portions of an asset at different profit rates. In this question, Sreya buys a plot, sells half of it at one profit percentage and the other half at a higher profit percentage. We must find the overall profit percentage on her entire investment. This requires computing the total selling price from both parts and comparing it with the total cost price.

Given Data / Assumptions:

• Total cost price of the plot = Rs. 6,00,000.
• Half of the plot is sold at 10% profit.
• The remaining half is sold at 15% profit.
• The halves are equal in cost because the plot is assumed uniform.
• We must find net profit percentage on the full Rs. 6,00,000.

Concept / Approach:
First, we split the total cost price into two equal parts, each corresponding to half of the plot. For each half, we compute the selling price by applying the given profit percentage: 10% on the first half and 15% on the second half. Adding these two selling prices gives the total selling price. The overall profit is total SP minus total CP. Finally, we divide the profit by the total CP and multiply by 100 to get the overall profit percentage. This is an example of a weighted average of profit percentages, but since both halves have equal cost, the computation is straightforward.

Step-by-Step Solution:
Step 1: Total cost price, CP_total = Rs. 6,00,000. Step 2: Cost of each half = 6,00,000 / 2 = Rs. 3,00,000. Step 3: First half is sold at 10% profit, so SP1 = 3,00,000 * 1.10 = Rs. 3,30,000. Step 4: Second half is sold at 15% profit, so SP2 = 3,00,000 * 1.15 = Rs. 3,45,000. Step 5: Total selling price, SP_total = SP1 + SP2 = 3,30,000 + 3,45,000 = Rs. 6,75,000. Step 6: Overall profit = SP_total - CP_total = 6,75,000 - 6,00,000 = Rs. 75,000. Step 7: Overall profit percentage = (75,000 / 6,00,000) * 100. Step 8: Simplify: 75,000 / 6,00,000 = 75 / 600 = 1 / 8, so profit percentage = (1/8) * 100 = 12.5%.

Verification / Alternative check:
Since both equal halves have the same cost, the overall profit percentage can also be seen as the simple average of 10% and 15%, which is (10 + 15) / 2 = 12.5%. This matches the detailed calculation. This shortcut works because the cost bases of both halves are identical; if they were different, we would need a weighted average based on cost values.

Why Other Options Are Wrong:
Values such as 13.8%, 11.4%, 14.5% or 10.5% do not equal the exact fraction 1/8 of the total cost price. Recomputing with those percentages would give total selling prices that differ from 6,75,000. Only 12.5% corresponds to an increase of Rs. 75,000 on Rs. 6,00,000.

Common Pitfalls:
A common mistake is to average the profit percentages even when the cost bases are not equal in other problems, leading to incorrect results. Here they happen to be equal, but learners should remember to check the cost distribution before averaging. Another error is to miscalculate 10% and 15% profits on Rs. 3,00,000 or to forget to sum the selling prices correctly.

Final Answer:
Sreya's overall profit percentage on the plot is 12.5 %.