$25^{\text {th }}$ Nov. 23
Q.) A man sold 2 bed sheats ₹ 400 each On one he gains $20 \%$ and on the other he loses $25 \%$ How much does he gain or lose in the whole transaction?

Step 1 ：Given that the selling price of each bed sheet is ₹400, one is sold at a gain of 20% and the other at a loss of 25%.

Step 2 ：First, we calculate the cost price for each bed sheet. The cost price for the bed sheet sold at a gain can be calculated using the formula \(\text{Cost Price} = \frac{\text{Selling Price}}{1 + \frac{\text{Gain Percentage}}{100}}\). Substituting the given values, we get \(\text{Cost Price} = \frac{400}{1 + \frac{20}{100}} = 333.33\)

Step 3 ：Similarly, the cost price for the bed sheet sold at a loss can be calculated using the formula \(\text{Cost Price} = \frac{\text{Selling Price}}{1 - \frac{\text{Loss Percentage}}{100}}\). Substituting the given values, we get \(\text{Cost Price} = \frac{400}{1 - \frac{25}{100}} = 533.33\)

Step 4 ：The total cost price for both the bed sheets is \(333.33 + 533.33 = 866.67\)

Step 5 ：The total selling price for both the bed sheets is \(400 + 400 = 800\)

Step 6 ：The overall gain or loss can be calculated by subtracting the total cost price from the total selling price. So, \(\text{Overall Gain/Loss} = \text{Total Selling Price} - \text{Total Cost Price} = 800 - 866.67 = -66.67\)

Step 7 ：Since the overall gain/loss is negative, it means there is a loss in the transaction.

Step 8 ：Final Answer: The man incurs a loss of \(\boxed{66.67}\) in the whole transaction.