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Sujatha sold 75% of her goods at a profi...

Sujatha sold 75% of her goods at a profit of 24% and the remaining at a loss of 40%. What is her gain/loss percentage on the whole transaction?

A

8% gain

B

10% gain

C

9% loss

D

7.5% loss

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will break it down step by step: ### Step 1: Understand the Distribution of Goods Sujatha sold 75% of her goods at a profit and the remaining 25% at a loss. Let’s assume the total cost of goods is \( C \). ### Step 2: Calculate the Amount Sold at Profit The amount sold at profit is: \[ \text{Amount sold at profit} = 75\% \text{ of } C = \frac{75}{100} \times C = 0.75C \] ### Step 3: Calculate Selling Price for Goods Sold at Profit The profit on these goods is 24%. Therefore, the selling price (SP) for this portion is: \[ \text{SP at profit} = \text{Cost Price} + \text{Profit} = 0.75C + 0.24 \times 0.75C \] \[ = 0.75C + 0.18C = 0.93C \] ### Step 4: Calculate the Amount Sold at Loss The remaining goods sold at a loss is: \[ \text{Amount sold at loss} = 25\% \text{ of } C = \frac{25}{100} \times C = 0.25C \] ### Step 5: Calculate Selling Price for Goods Sold at Loss The loss on these goods is 40%. Therefore, the selling price for this portion is: \[ \text{SP at loss} = \text{Cost Price} - \text{Loss} = 0.25C - 0.40 \times 0.25C \] \[ = 0.25C - 0.10C = 0.15C \] ### Step 6: Calculate Total Selling Price Now, we can find the total selling price (SP) for all goods: \[ \text{Total SP} = \text{SP at profit} + \text{SP at loss} = 0.93C + 0.15C = 1.08C \] ### Step 7: Calculate Total Cost Price The total cost price (CP) of all goods is simply \( C \). ### Step 8: Calculate Gain or Loss Now we can determine the overall gain or loss: \[ \text{Gain} = \text{Total SP} - \text{Total CP} = 1.08C - C = 0.08C \] ### Step 9: Calculate Gain Percentage To find the gain percentage: \[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{Total CP}} \right) \times 100 = \left( \frac{0.08C}{C} \right) \times 100 = 8\% \] ### Final Answer Sujatha's overall gain percentage on the whole transaction is **8%**. ---
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