A shopkeeper sells one transistor for ₹ 840 at a gain of $20\%$ and another for ₹ 960 at a loss of $4\%$. His total gain or loss percent is

### Concept & Aggregate Profit and Loss To find the overall profit or loss percentage, you must find the total Cost Price (CP) of all items and the total Selling Price (SP) of all items. $$ \text{Overall Profit or Loss \%} = \frac{\text{Total SP} - \text{Total CP}}{\text{Total CP}} \times 100 $$ ### Step-by-Step Solution * Transaction 1: SP1 = ₹ 840, Gain = $20\%$ * CP1 = $\frac{840}{1 + 0.20} = \frac{840}{1.2} = \text{₹ } 700$ * Transaction 2: SP2 = ₹ 960, Loss = $4\%$ * CP2 = $\frac{960}{1 - 0.04} = \frac{960}{0.96} = \text{₹ } 1000$ * Find Total Cost Price: Total CP = $CP1 + CP2 = 700 + 1000 = \text{₹ } 1700$ * Find Total Selling Price: Total SP = $SP1 + SP2 = 840 + 960 = \text{₹ } 1800$ * Since Total SP > Total CP, there is an overall gain. * Total Gain = $1800 - 1700 = \text{₹ } 100$ * Overall Gain \% = $(\frac{100}{1700}) \times 100 = \frac{100}{17}\%$ * Convert to mixed fraction: $100 \div 17 = 5$ with a remainder of $15$. Thus, $5 \frac{15}{17}\%$. ### Exam Strategy & Shortcut Work with multipliers quickly. $1.2 \times CP1 = 840 \rightarrow CP1 = 700$. $0.96 \times CP2 = 960 \rightarrow CP2 = 1000$. Total investment is $1700$, total return is $1800$. The profit is $100$ over $1700$. Fraction is $1/17$. Since $1/17 \approx 5.88\%$, check options: $5 \frac{15}{17}\%$ matches perfectly. ### Common Pitfall Averaging the two percentage values (e.g., $+20\%$ and $-4\%$). You cannot average percentages directly when the base Cost Prices are different. You must calculate total CP and total SP. ### Final Answer Therefore, the correct answer is **$5 \frac{15}{17}\%$ gain**.