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Question
A retailer buys an article at a discount of 20% on the listed price from a wholesaler. The shopkeeper marks up the price by 10% on the listed price. A buyer pays Rs 231 to get it after paying a sales tax at the rate of 5% on the price asked for. Find the profit percentage.
Solution
Let listed price be x. Rebate on listed price = 20 % of listed price
Rebated price = x - 20 % of x
= `x - (20 x)/100`
= `(80 x)/100` ............(i)
Effective marked price = listed price + 10 % of listed price
= `x + 10/100 xx x`
= `(110 x)/100`
Sales tax = 5 % of the effective marked price
= `5/100 xx "Rs" (110 x)/100`
= Rs `(55 x)/1000`
Total cost =
= Rs `(110 x)/100 + "Rs" (5 x)/1000`
= `(1105 x)/1000`
But total cost = Rs 231
⇒ `(1105 x)/1000` = Rs 231
⇒ 1105 x = Rs231000
⇒ x = Rs 209. 04
Listed price = Rs 209
Cost price for shopkeeper = `(80 x)/100` .................(from (i))
= Rs `80/100 xx 209`
= Rs 167.20
Effective marked price = `(110 x)/100` ...................(from (ii))
= Rs `110/100 xx 209`
= Rs 229.90
His profit = (effective marked price - rebated cost price)
=Rs (229.90-167.20) =Rs 62.70
His profit percentage = `62.70/167.20 xx 100 = 37.5 %`
Hence, his profit percentage = 37.5 %
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