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Question
A retailer sold a suit for ₹ 8,832 after allowing 8% discount on marked price and further 4% cash discount. If he made 38% profit, find the cost price and the marked price of the suit.
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Solution
Let the marked price of the suit be ‘x’.
Seller allows discount of 8% on marked price.
∴ Discount = `x xx 8/100 = 0.08"x"`
∴ Net price = x – 0.08x = 0.92x
Further cash discount of 4% is given.
∴ Cash discount `= 0.92 x xx 4/100 = 0.0368 x`
∴ Net selling price = 0.92x – 0.0368x = 0.8832x
However, net selling price is given as ₹ 8,832.
∴ 0.8832x = 8832
∴ x = `8832/0.8832`
∴ x = ₹ 10000
∴ Marked price (list price) ₹ 10,000.
Retailer has made 38% profit on cost price.
Let the cost price be y.
Profit `= y xx 38/100 = (38y)/100`
Cost price + Profit = Selling price
∴ `y + (38y)/100 = 8,832`
∴ `(100y + 38y)/100 = 8,832`
∴ `(138y)/100 = 8,832`
∴ y = `(8,832 xx 100)/138` = ₹ 6400
∴ The cost price of the suit is ₹ 6,400 and list price (marked price) is ₹ 10,000.
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