A shopkeeper buys 144 eggs at 90 paise each. On the way 20 eggs were broken. He sold the remaining eggs at ₹ 1.20 each. The percentage gain or loss is

### Concept & Total Cost vs. Total Revenue To find the true overall profit or loss percentage, you must compare the Total Cost Price incurred (for all items, regardless of condition) against the Total Selling Revenue generated (from the items actually sold). $$ \text{Overall \%} = \left( \frac{\text{Total Revenue} - \text{Total Cost}}{\text{Total Cost}} \right) \times 100 $$ ### Step-by-Step Solution * **Step 1:** Calculate the Total Cost Price (CP). * Total eggs bought = 144 * Price per egg = 90 paise = ₹ 0.90 * $\text{Total CP} = 144 \times 0.90 = ₹ 129.60$ * **Step 2:** Calculate the saleable inventory. * Broken eggs = 20 * Remaining eggs = $144 - 20 = 124$ eggs * **Step 3:** Calculate the Total Selling Price (SP). * Selling price per egg = ₹ 1.20 * $\text{Total SP} = 124 \times 1.20$ * $\text{Total SP} = 124 \times \frac{6}{5} = \frac{744}{5} = ₹ 148.80$ * **Step 4:** Determine Gain or Loss Amount. * Since Total SP (148.80) > Total CP (129.60), there is a gain. * $\text{Gain} = 148.80 - 129.60 = ₹ 19.20$ * **Step 5:** Calculate Gain Percentage. * $\text{Gain \%} = \left(\frac{19.20}{129.60}\right) \times 100$ * Remove decimals: $\left(\frac{192}{1296}\right) \times 100$ * Simplify fraction: Divide by 4 $\rightarrow \frac{48}{324}$; Divide by 12 $\rightarrow \frac{4}{27}$ * $\text{Gain \%} = \frac{400}{27} \approx 14.814...\%$ * Rounding to one decimal place, the gain is $14.8\%$. ### Exam Strategy & Shortcut Work purely in ratios to avoid large decimals. $\text{Total CP} = 144 \times 9 = 1296$ (working in units of 10 paise to keep numbers clean). $\text{Total SP} = 124 \times 12 = 1488$. $\text{Ratio of CP : SP} = 1296 : 1488$. Divide by 24 $\rightarrow 54 : 62 \rightarrow 27 : 31$. A jump from 27 to 31 is an increase of 4. $\frac{4}{27} \times 100 \approx 14.8\%$. ### Common Pitfall Calculating the profit per egg by comparing the initial 90 paise to the final ₹1.20 while completely ignoring the sunk cost of the 20 broken eggs. You must use aggregate totals. ### Final Answer Therefore, the correct answer is **14.8% gain**.