A fruitseller sells mangoes at the rate of ₹ 9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%?

### Concept & Proportional Selling Prices When dealing with two selling prices where one results in a loss and the other in a profit, their values are strictly proportional to their respective percentages relative to the Cost Price. $$ \frac{SP_1}{100 - L_1} = \frac{SP_2}{100 + P_2} $$ ### Step-by-Step Solution * **Establish the Initial Condition:** * Given $SP_1 = 9$ per kg. * Resulting loss = $20\%$. * Therefore, ₹ 9 represents $80\%$ ($100\% - 20\%$) of the true Cost Price (CP). * **Determine the Target Condition:** * Target profit = $5\%$. * The new Selling Price ($SP_2$) must represent $105\%$ ($100\% + 5\%$) of the Cost Price. * **Calculate New Selling Price:** * Set up the equation based on the proportionality: $\frac{9}{80} = \frac{SP_2}{105}$. * $SP_2 = \frac{9 \times 105}{80}$ * Simplify the fraction by dividing 105 and 80 by 5: $\frac{105}{80} = \frac{21}{16}$. * $SP_2 = \frac{9 \times 21}{16} = \frac{189}{16}$. * $SP_2 = 11.8125$ rupees. ### Exam Strategy & Shortcut Skip calculating the exact CP (₹ 11.25) to save time. Just write $9 \times \left(\frac{105}{80}\right)$. Simplify to $9 \times \left(\frac{21}{16}\right)$. $189 \div 16$ is slightly less than $192 \div 16$ (which is exactly 12). Since $189$ is $3$ less than $192$, it is $12 - \frac{3}{16}$. Since $\frac{1}{16}$ is roughly $0.06$, $\frac{3}{16}$ is about $0.18$. $12 - 0.18 = 11.82$. Option (a) is the only mathematical match. ### Common Pitfall Calculating the $20\%$ loss based on the selling price (₹ 9) rather than the cost price, which mathematically corrupts the baseline needed to compute the required $5\%$ profit. ### Final Answer Therefore, the correct answer is **₹ 11.81**.