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A shopkeeper sold some bedsheets of one ...

A shopkeeper sold some bedsheets of one variety for Rs.12,000 for 20% profit, and some bedsheets of another variety for Rs.10,350 for 15% profit. What was his overall profit on the sale of these bedsheets?

A

Rs. 3,750

B

Rs. 3,350

C

Rs. 552.50

D

Rs. 3,952.50

Text Solution

AI Generated Solution

The correct Answer is:
To find the overall profit on the sale of the bedsheets, we can follow these steps: ### Step 1: Calculate the Cost Price (CP) of the first variety of bedsheets. The selling price (SP) of the first variety is Rs. 12,000, and the profit percentage is 20%. Using the formula: \[ \text{SP} = \text{CP} + \text{Profit} \] where Profit = \(\frac{\text{Profit \%}}{100} \times \text{CP}\). We can rearrange this to find CP: \[ \text{SP} = \text{CP} + \left(\frac{20}{100} \times \text{CP}\right) = \text{CP} \left(1 + \frac{20}{100}\right) = \text{CP} \left(\frac{120}{100}\right) \] \[ \text{CP} = \frac{\text{SP}}{1.2} = \frac{12000}{1.2} = 10000 \] ### Step 2: Calculate the Cost Price (CP) of the second variety of bedsheets. The selling price (SP) of the second variety is Rs. 10,350, and the profit percentage is 15%. Using the same approach: \[ \text{SP} = \text{CP} + \left(\frac{15}{100} \times \text{CP}\right) = \text{CP} \left(1 + \frac{15}{100}\right) = \text{CP} \left(\frac{115}{100}\right) \] \[ \text{CP} = \frac{\text{SP}}{1.15} = \frac{10350}{1.15} = 9000 \] ### Step 3: Calculate the total Cost Price (CP) and total Selling Price (SP). Total CP = CP of first variety + CP of second variety \[ \text{Total CP} = 10000 + 9000 = 19000 \] Total SP = SP of first variety + SP of second variety \[ \text{Total SP} = 12000 + 10350 = 22350 \] ### Step 4: Calculate the overall profit. Overall Profit = Total SP - Total CP \[ \text{Overall Profit} = 22350 - 19000 = 3350 \] ### Final Result: The overall profit on the sale of these bedsheets is Rs. 3,350. ---
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