Calculating Overall Profit Percentage
Let the total Cost Price (CP) of the goods be \(100\). We can break down the calculation based on the proportions sold at different profit/loss margins.
Step 1: Calculate Sales from the First Batch
- Percentage of goods sold: \(44\%\)
- CP of this batch: \(44\% \text{ of } 100 = \)44$
- Profit percentage: \(28\%\)
- Selling Price (SP) of this batch: \(44 \times (1 + \frac{28}{100}) = 44 \times 1.28 = \)56.32$
- Profit from this batch: \(56.32 - 44 = \)12.32$
Step 2: Calculate Sales from the Second Batch
- Remaining goods: \(100 - 44 = 56\)
- Percentage of remaining goods sold: \(25\%\)
- Quantity of goods in this batch: \(25\% \text{ of } 56 = 0.25 \times 56 = 14\)
- CP of this batch: \(14\% \text{ of } 100 = \)14$
- Profit percentage: \(48\%\)
- SP of this batch: \(14 \times (1 + \frac{48}{100}) = 14 \times 1.48 = \)20.72$
- Profit from this batch: \(20.72 - 14 = \)6.72$
Step 3: Calculate Sales from the Third Batch
- Remaining goods after the second batch: \(56 - 14 = 42\)
- CP of this batch: \(42\% \text{ of } 100 = \)42$
- Loss percentage: \(18\%\)
- SP of this batch: \(42 \times (1 - \frac{18}{100}) = 42 \times 0.82 = \)34.44$
- Loss from this batch: \(42 - 34.44 = \)7.56$
Step 4: Calculate Overall Profit
- Total CP = \(44 + 14 + 42 = \)100$
- Total SP = \(56.32 + 20.72 + 34.44 = \)111.48$
- Overall Profit = Total SP - Total CP = \(111.48 - 100 = \)11.48$
- Overall Profit Percentage (x%) = \(\frac{\text{Overall Profit}}{\text{Total CP}} \times 100\)
- \(x\% = \frac{11.48}{100} \times 100 = 11.48\%\)
The overall profit is \(11.48\%\). Thus, \(x = 11.48\).
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Important Questions from Profit and Loss
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