Shailja earns 15 percent on an investment but loses 10 percent on another investment. If the ratio of the two investments is $3 : 5$, then the combined loss percent is (S.S.C., 2006)

### Concept & Weighted Average Profit/Loss When different investments yield different returns (profits or losses), the overall return percentage is the weighted average of the individual returns, using the investment amounts as weights. $$ \text{Combined Return } \% = \frac{\text{Total Profit/Loss}}{\text{Total Investment}} \times 100 $$ ### Step-by-Step Solution * The ratio of the two investments is $3 : 5$. * Let the two investments be $3x$ and $5x$. * Total Investment = $3x + 5x = 8x$. * Return on the first investment (15% profit): Profit = $15\%$ of $3x = 0.15 \times 3x = +0.45x$ * Return on the second investment (10% loss): Loss = $10\%$ of $5x = 0.10 \times 5x = -0.50x$ * Net Return (Combined Profit/Loss): Net = $+0.45x - 0.50x = -0.05x$ * Since the net result is negative, it is an overall loss. * Combined Loss Percent = $\frac{\text{Net Loss}}{\text{Total Investment}} \times 100$ * Loss Percent = $\left(\frac{0.05x}{8x}\right) \times 100 = \frac{0.05}{8} \times 100 = \frac{5}{8}\%$ ### Exam Strategy & Shortcut Use base numbers for ratios. Let the investments be 300 and 500. Total = 800. $15\%$ of 300 = +45. $10\%$ of 500 = -50. Net = -5. Loss percent = $\frac{5}{800} \times 100 = \frac{5}{8}\%$. This avoids decimals entirely. ### Common Pitfall Simply averaging the percentages ($15\% - 10\% = 5\%$) without factoring in the weight (ratio) of the respective investments. ### Final Answer Therefore, the correct answer is **$\frac{5}{8}$**.