If by selling 110 mangoes, the C.P. of 120 mangoes is realised, the gain percent is

### Concept & Formula When the cost price of $a$ articles is recovered by selling $b$ articles, the profit or loss depends on the difference between the quantities. $$ \text{Gain \%} = \frac{\text{Goods Left}}{\text{Goods Sold}} \times 100 = \frac{a - b}{b} \times 100 $$ ### Step-by-Step Solution 1. Let the Cost Price (CP) of 1 mango be $1. 2. The CP of 120 mangoes is $120. 3. The Selling Price (SP) of 110 mangoes equals the CP of 120 mangoes, which is $120. 4. The CP of the 110 mangoes actually sold is $110. 5. Gain = SP of 110 mangoes - CP of 110 mangoes = $120 - $110 = $10. 6. Gain % = $(\text{Gain} / \text{CP}) \times 100 = (10 / 110) \times 100 = \frac{100}{11}\%$. 7. Convert to a mixed fraction: $9 \frac{1}{11}\%$. ### Exam Strategy & Shortcut Use the direct quantity formula: $\text{Gain \%} = \frac{120 - 110}{110} \times 100 = \frac{10}{110} \times 100 = 9 \frac{1}{11}\%$. ### Common Pitfall A common error is dividing the difference (10) by the total quantity (120) instead of the quantity sold (110). Profit is realized on the items actually sold. ### Final Answer Therefore, the correct answer is **$9 \frac{1}{11}\%$**.