6. Mwilaria a businessman makes a profit of \( 2 \% \) \% when he sels a carpet for sh 36000 . At a frade fair he sad suich a carpet at sh 33600 a) Calculate the percentage profit made on the sale of the carpet during the trade fair b) At the trade fair he had 6o such carpets If he sold e/3 of the carpet, how much profit did he make

To solve the problem, we will break it down into two parts: ### Part (a): Calculate the percentage profit made on the sale of the carpet during the trade fair. 1. **Determine the cost price (CP) of the carpet:** - Mwilaria makes a profit of \(2\%\) when he sells the carpet for \(sh 36,000\). - Let the cost price be \(CP\). - The selling price (SP) is given by the formula: \[ SP = CP + (2\% \text{ of } CP) \] - This can be rewritten as: \[ SP = CP \times (1 + \frac{2}{100}) = CP \times 1.02 \] - Setting the selling price equal to \(sh 36,000\): \[ 36000 = CP \times 1.02 \] - Solving for \(CP\): \[ CP = \frac{36000}{1.02} \approx 35294.12 \] 2. **Calculate the profit made during the trade fair:** - The selling price at the trade fair is \(sh 33,600\). - The profit made during the trade fair is: \[ \text{Profit} = SP - CP = 33600 - 35294.12 \approx -1694.12 \] - Since the profit is negative, it indicates a loss. 3. **Calculate the percentage loss:** - The percentage loss can be calculated using the formula: \[ \text{Percentage Loss} = \left(\frac{\text{Loss}}{CP}\right) \times 100 \] - Substituting the values: \[ \text{Percentage Loss} = \left(\frac{1694.12}{35294.12}\right) \times 100 \approx 4.79\% \] ### Part (b): Calculate the profit made from selling \( \frac{1}{3} \) of the carpets. 1. **Determine how many carpets were sold:** - Mwilaria had \(60\) carpets and sold \( \frac{1}{3} \) of them: \[ \text{Number of carpets sold} = \frac{1}{3} \times 60 = 20 \] 2. **Calculate the total cost price for the \(20\) carpets:** - The cost price of one carpet is approximately \(sh 35,294.12\). - Therefore, the total cost price for \(20\) carpets is: \[ \text{Total CP} = 20 \times 35294.12 \approx 705882.4 \] 3. **Calculate the total selling price for the \(20\) carpets:** - The selling price for one carpet at the trade fair is \(sh 33,600\). - Therefore, the total selling price for \(20\) carpets is: \[ \text{Total SP} = 20 \times 33600 = 672000 \] 4. **Calculate the total profit made:** - The total profit is given by: \[ \text{Total Profit} = \text{Total SP} - \text{Total CP} = 672000 - 705882.4 \approx -33882.4 \] - This indicates a loss. ### Summary of Results: - **Part (a):** The percentage loss made during the trade fair is approximately \(4.79\%\). - **Part (b):** The total loss made from selling \( \frac{1}{3} \) of the carpets is approximately \(sh 33,882.4\).