Alfred buys an old scooter for ₹ 4700 and spends ₹ 800 on its repairs. If he sells the scooter for ₹ 5800, his gain percent is

### Concept & True Cost Price Before calculating profit or loss percentages, any money spent on repairs, maintenance, or upgrades immediately after purchase must be added to the raw purchase price to establish the "True" or "Effective" Cost Price. $$ \text{Gain \%} = \left( \frac{\text{SP} - \text{True CP}}{\text{True CP}} \right) \times 100 $$ ### Step-by-Step Solution Given: * Purchase Price = ₹ 4700 * Repair Cost = ₹ 800 * Selling Price (SP) = ₹ 5800 Calculation: 1. Find the True Cost Price (CP). $$ \text{True CP} = 4700 + 800 = 5500 $$ 2. Calculate the gain (profit). $$ \text{Gain} = \text{SP} - \text{True CP} = 5800 - 5500 = 300 $$ 3. Calculate the gain percentage based on the True CP. $$ \text{Gain \%} = \left(\frac{300}{5500}\right) \times 100 $$ 4. Simplify the fraction. $$ \text{Gain \%} = \frac{300}{55} = \frac{60}{11} $$ 5. Convert the improper fraction to a mixed number. $$ \frac{60}{11} = 5 \text{ with a remainder of } 5 = 5\frac{5}{11}\% $$ ### Exam Strategy & Shortcut Whenever dealing with numbers ending in double zeros (300, 5500), immediately mentally strike them out to simplify the ratio to $3/55$. Then multiply by 100: $300/55 \rightarrow 60/11$. Knowing your fraction-to-mixed-number conversions makes $60/11$ instantly recognizable as $5\frac{5}{11}\%$. ### Common Pitfall The most common mistake is ignoring the repair costs and using ₹ 4700 as the denominator. This would result in a gain of $1100 / 4700$, leading to a completely incorrect percentage. Always consolidate costs first. ### Final Answer Therefore, the correct answer is **(b) $5\frac{5}{11}\%$**.