Question
Download Solution PDFWhen an item is sold at a price of Rs.11000 then the profit made on it is 20% more than the loss incurred when the same item is sold at Rs.5500. Find the purchase price of the item.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Selling Price 1 (SP1) = Rs. 11000, which results in a profit.
Selling Price 2 (SP2) = Rs. 5500, which results in a loss.
The profit made on SP1 is 20% more than the loss incurred on SP2.
Formula used:
Profit = Selling Price - Cost Price (SP - CP)
Loss = Cost Price - Selling Price (CP - SP)
Calculations:
Let the Cost Price (CP) of the item be 'x' Rupees.
Case 1: Item sold at Rs. 11000 (Profit)
Profit = SP1 - CP
⇒ Profit = 11000 - x
Case 2: Item sold at Rs. 5500 (Loss)
Loss = CP - SP2
⇒ Loss = x - 5500
Relationship between Profit and Loss:
Profit = Loss + 20% of Loss
⇒ Profit = Loss + (20/100) × Loss
⇒ Profit = Loss + 0.20 × Loss
⇒ Profit = 1.20 × Loss
Now, substitute the expressions for Profit and Loss into this equation:
11000 - x = 1.20 × (x - 5500)
11000 - x = 1.20x - (1.20 × 5500)
11000 - x = 1.20x - 6600
11000 + 6600 = 1.20x + x
17600 = 2.20x
x = 17600 / 2.20
x = 8000
∴ The purchase price of the item is Rs. 8000.
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