Raghu earns a profit of 25 percent on one investment but incurs a loss of 10 percent on another investment. The ratio of the amounts invested in the two cases is 3 : 5 respectively. What is the overall percentage gain or loss on both investments taken together?

Introduction / Context:
This question examines the idea of overall profit or loss when different parts of capital are invested at different profit or loss percentages. The key is to treat the problem as a weighted average percentage gain or loss, based on the proportions of total capital invested in each case.

Given Data / Assumptions:

• Profit on the first investment = 25 percent.
• Loss on the second investment = 10 percent.
• Ratio of the first investment to the second investment = 3 : 5.
• We assume the same time period and no other costs or incomes.

Concept / Approach:
When there are two investments with different profit rates, the overall profit is the sum of the individual profits. Because the invested amounts are in a ratio, we can assume convenient values proportional to that ratio, such as 3x and 5x. Then, compute individual profit or loss in terms of x, add them, and finally divide by total investment to get the overall percentage gain or loss.

Step-by-Step Solution:
Assume first investment = 3x and second investment = 5x. Profit on the first investment = 25 percent of 3x = 0.25 * 3x = 0.75x. Loss on the second investment = 10 percent of 5x = 0.10 * 5x = 0.50x. Net profit = profit - loss = 0.75x - 0.50x = 0.25x. Total capital invested = 3x + 5x = 8x. Overall percentage gain = (net profit / total capital) * 100. Overall gain percent = (0.25x / 8x) * 100 = (0.25 / 8) * 100. 0.25 / 8 = 0.03125, so overall gain = 3.125 percent.

Verification / Alternative check:
Take x = 1000 for convenience. First investment = Rs. 3000, profit = 25 percent of 3000 = Rs. 750. Second investment = Rs. 5000, loss = 10 percent of 5000 = Rs. 500. Net profit = 750 - 500 = Rs. 250. Total investment = 3000 + 5000 = Rs. 8000. Overall gain percent = 250 / 8000 * 100 = 3.125 percent. This confirms the result.

Why Other Options Are Wrong:
1.251 % and 7.21 % and 9.451 %: These values do not correspond to the correct weighted average calculation using the given ratio 3 : 5. They usually come from incorrect manipulation of percentages or from averaging the rates without considering the different investment amounts.

Common Pitfalls:
A common error is to average 25 percent and minus 10 percent directly to get 7.5 percent, which ignores the investment ratio. Another typical mistake is to treat the loss percentage as if it were on the same base amount as the profit percentage. Always use assumed values based on the given ratio to create a consistent base for both investments.

Final Answer:
The overall result is a net gain of 3.125 % on the combined investments.