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8 boxes of a fruit were purchased for Rs...

8 boxes of a fruit were purchased for Rs 9,600.5 boxes were sold at a profit of 10% and 3 boxes were sold at a loss of 10%. What is the net gain in percentage ?

A

`2.75 %`

B

`2.5%`

C

`2%`

D

`2.25%`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, let's break it down: ### Step 1: Determine the Cost Price (CP) of one box The total cost of 8 boxes is Rs 9,600. Therefore, the cost price of one box can be calculated as follows: \[ \text{CP of one box} = \frac{\text{Total Cost}}{\text{Number of Boxes}} = \frac{9600}{8} = 1200 \text{ Rs} \] ### Step 2: Calculate the Selling Price (SP) of the 5 boxes sold at a profit of 10% If 5 boxes are sold at a profit of 10%, we first need to find the selling price of one box at this profit: \[ \text{SP of one box at 10% profit} = \text{CP} + 10\% \text{ of CP = } 1200 + (0.10 \times 1200) = 1200 + 120 = 1320 \text{ Rs} \] Now, for 5 boxes: \[ \text{SP of 5 boxes} = 5 \times 1320 = 6600 \text{ Rs} \] ### Step 3: Calculate the Selling Price (SP) of the 3 boxes sold at a loss of 10% Now, for the 3 boxes sold at a loss of 10%, we find the selling price of one box at this loss: \[ \text{SP of one box at 10% loss} = \text{CP} - 10\% \text{ of CP = } 1200 - (0.10 \times 1200) = 1200 - 120 = 1080 \text{ Rs} \] Now, for 3 boxes: \[ \text{SP of 3 boxes} = 3 \times 1080 = 3240 \text{ Rs} \] ### Step 4: Calculate the Total Selling Price (SP) Now we can find the total selling price of all 8 boxes: \[ \text{Total SP} = \text{SP of 5 boxes} + \text{SP of 3 boxes} = 6600 + 3240 = 9840 \text{ Rs} \] ### Step 5: Calculate the Net Gain To find the net gain, we subtract the total cost price from the total selling price: \[ \text{Net Gain} = \text{Total SP} - \text{Total CP} = 9840 - 9600 = 240 \text{ Rs} \] ### Step 6: Calculate the Gain Percentage Finally, we can calculate the gain percentage using the formula: \[ \text{Gain Percentage} = \left( \frac{\text{Net Gain}}{\text{Total CP}} \right) \times 100 = \left( \frac{240}{9600} \right) \times 100 = 2.5\% \] ### Final Answer The net gain percentage is **2.5%**. ---
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