Question
Download Solution PDFA trader sells one item to a retailer at a 20% discount, but charges 10% on the discounted price, for delivery and packaging. The retailer sells it for ₹ 4,092 more, thereby earning a profit of 25% At what price had the trader marked the item?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Marked price (MP) = ?
Discount = 20%
Charges for delivery and packaging = 10% on discounted price
Retailer's selling price (SP) = ₹ 4,092 more
Retailer's profit = 25%
Formula used:
Discounted price (DP) = MP × (1 - Discount%)
Selling Price by Trader (SPT) = DP × (1 + Charges%)
Cost Price for Retailer (CPR) = SPT
Retailer's Selling Price (RSP) = CPR × (1 + Profit%)
Difference in price = RSP - CPR
Calculation:
Let the marked price be MP = x
⇒ Discounted price DP = x × (1 - 0.20)
⇒ DP = 0.80x
⇒ SPT = 0.80x × (1 + 0.10)
⇒ SPT = 0.80x × 1.10
⇒ SPT = 0.88x
Retailer's Selling Price (RSP) = 0.88x × (1 + 0.25)
⇒ RSP = 0.88x × 1.25
⇒ RSP = 1.10x
Given that the retailer sells it for ₹ 4,092 more:
⇒ 1.10x - 0.88x = 4092
⇒ 0.22x = 4092
⇒ x = 4092 / 0.22
⇒ x = 18,600
∴ The correct answer is option 2.
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