A shopkeeper bought $56$ dozen eggs at ₹$2.50$ per egg. $120$ eggs broke in transportation. He sold the remaining eggs at ₹$2.75$ each. What is his profit or loss per cent?

Step 1: Calculate Total Cost Price (CP)Total number of eggs bought = $56\times 12=672\text{ eggs}$ Cost per egg = ₹$2.50$ Total Cost Price ($\text{CP}$) = $672\times 2.50=672\times \frac{5}{2}=336\times 5=$ ₹$1,680$ Step 2: Calculate Total Selling Price (SP)Number of broken eggs = $120$ Remaining good eggs = $672-120=552\text{ eggs}$ Selling price per egg = ₹$2.75$ Total Selling Price ($\text{SP}$) = $552\times 2.75=552\times \frac{11}{4}=138\times 11=$ ₹$1,518$ Step 3: Calculate Profit or LossSince $\text{CP}>\text{SP}$, it is a loss.$\text{Loss}=\text{CP}-\text{SP}=1680-1518=$ ₹$162$ Step 4: Calculate Loss Percentage
$$\text{Loss }\%=\left(\frac{\text{Loss}}{\text{CP}}\right)\times 100$$
$$\text{Loss }\%=\frac{162}{1680}\times 100=\frac{1620}{168}=\frac{135}{14}=9\frac{9}{14}\%$$
Thus, there is a loss of $9\frac{9}{14}\%$.