Sure, let's solve this problem step by step.
Step 1: Calculate the discount amount
The marked price of the shirt is sh. 1800 and there's a discount of 10%.
[tex]\[
\text{Discount amount} = \text{Marked price} \times \frac{\text{Discount percentage}}{100}
\][/tex]
[tex]\[
\text{Discount amount} = 1800 \times \frac{10}{100} = 180.0 \text{ shillings}
\][/tex]
Step 2: Calculate the selling price
The selling price is the marked price minus the discount amount.
[tex]\[
\text{Selling price} = \text{Marked price} - \text{Discount amount}
\][/tex]
[tex]\[
\text{Selling price} = 1800 - 180 = 1620.0 \text{ shillings}
\][/tex]
Step 3: Calculate the cost price
We know the trader made a profit of sh. 324. The cost price can be calculated by subtracting the profit from the selling price.
[tex]\[
\text{Cost price} = \text{Selling price} - \text{Profit}
\][/tex]
[tex]\[
\text{Cost price} = 1620 - 324 = 1296.0 \text{ shillings}
\][/tex]
Step 4: Calculate the percentage profit
The percentage profit is given by the profit divided by the cost price, multiplied by 100.
[tex]\[
\text{Percentage profit} = \left(\frac{\text{Profit}}{\text{Cost price}}\right) \times 100
\][/tex]
[tex]\[
\text{Percentage profit} = \left(\frac{324}{1296}\right) \times 100 = 25.0\%
\][/tex]
Final Answer:
The percentage profit is [tex]\(25.0\%\)[/tex].
