A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?

### Concept & Formula The relationship between Cost Price (CP), Selling Price (SP), and profit percentage can be calculated per single item. $$SP = CP \times \left(1 + \frac{\text{Profit } \%}{100}\right)$$ ### Step-by-Step Solution * **Given:** CP rate = 6 toffees for ₹ 1. Desired Gain = 20%. * **Calculation:** 1. CP of 1 toffee = $\text{₹ } \frac{1}{6}$ 2. Desired SP of 1 toffee for a 20% gain = $CP \times 1.20 = \left(\frac{1}{6}\right) \times \left(\frac{120}{100}\right)$ 3. Simplify the multiplier: $\frac{120}{100} = \frac{6}{5}$ 4. SP of 1 toffee = $\left(\frac{1}{6}\right) \times \left(\frac{6}{5}\right) = \text{₹ } \frac{1}{5}$ 5. This means 1 toffee is sold for ₹ $\frac{1}{5}$. Therefore, for ₹ 1, he must sell 5 toffees. ### Exam Strategy & Shortcut Use the inverse relationship between price and quantity. If price per item increases to gain profit, the quantity sold for a fixed amount (₹ 1) must decrease. Quantity to sell = Buy Quantity $\times \frac{100}{100 + \text{Profit } \%} = 6 \times \frac{100}{120} = 6 \times \frac{5}{6} = 5$. ### Common Pitfall Calculating 20% of 6 and adding it to 6 (getting 7.2) or subtracting it (getting 4.8). The percentage applies to the monetary value, which inversely affects the quantity for a fixed amount. ### Final Answer Therefore, the correct answer is **5**.