$$\text{A dealer purchases 1,200 eggs at ₹4.50 each. During transit, 8\% of the eggs break. The remaining eggs are sold at ₹6.00 each. Find the overall profit percentage. }$$

The correct option is:

$22\frac{2}{3}\%$

Here is the step-by-step logical explanation of the solution:
First, let's understand the two major stages of the transaction: purchasing the eggs (Cost Price) and selling the remaining unbroken eggs (Selling Price).

Step 1: Calculate the Total Cost Price (CP)
The dealer purchased 1,200 eggs at ₹4.50 each. We calculate the total amount spent as follows:

$$\text{Total Cost Price (CP)}=\mathrm{1,200}\times 4.50=\text{₹}\mathrm{5,400}$$

Step 2: Calculate the number of broken eggs and remaining eggs
During transit, 8% of the eggs were broken. Let's find the number of broken eggs:

$$\text{Broken eggs}=8\%\text{of}\mathrm{1,200}=\frac{8}{100}\times \mathrm{1,200}=96$$

Subtracting the broken eggs from the initial amount gives the number of eggs remaining to be sold:

$$\text{Remaining eggs}=\mathrm{1,200}-96=\mathrm{1,104}$$

Step 3: Calculate the Total Selling Price (SP)
The remaining 1,104 eggs are sold at a rate of ₹6.00 each. The total revenue generated is:

$$\text{Total Selling Price (SP)}=\mathrm{1,104}\times 6.00=\text{₹}\mathrm{6,624}$$

Step 4: Find the Overall Profit
We subtract the Total Cost Price from the Total Selling Price to find the profit:

$$\text{Profit}=\text{Total SP}-\text{Total CP}$$

$$\text{Profit}=\mathrm{6,624}-\mathrm{5,400}=\text{₹}\mathrm{1,224}$$

Step 5: Calculate the Overall Profit Percentage
The profit percentage is calculated relative to the Cost Price:

$$\text{Profit Percentage}=\left(\frac{\text{Profit}}{\text{Total CP}}\right)\times 100\%$$

$$\text{Profit Percentage}=\frac{\mathrm{1,224}}{\mathrm{5,400}}\times 100\%=\frac{\mathrm{1,224}}{54}\%$$

Simplifying the fraction by dividing both the numerator and the denominator by 18, we get:

$$\text{Profit Percentage}=\frac{68}{3}\%$$

Converting this improper fraction to a mixed fraction, we divide 68 by 3 which equals 22 with a remainder of 2:

$$\text{Profit Percentage}=22\frac{2}{3}\%$$