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Question
A retailer buys an article at a discount of 15% on the printed price from a wholesaler. He marks up the price by 10%. Due to competition in the market, he allows a discount of 5% to a buyer. If the buyer pays ₹451.44 for the article inclusive of sales tax (under VAT) at 8%, find :
(i) the printed price of the article
(ii) the profit percentage of the retailer.
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Solution
(i) Let the printed price of the article = ₹100
Then, retailer’s cost price
= ₹100-₹15 = ₹85
Now, marked price for the retailer
= ₹100 + ₹10 = ₹110
Rate of discount allowed = 5%
∴ Sale price
= `₹(110 xx (100 - 5))/(100)`
= `₹(110 xx 95)/(100)`
= `₹(1045)/(10)`
∴ Sale price including sales tax
= `₹(1045)/(10) xx (100 + 8)/(100)`
= `₹(1045 xx 108)/(1000)`
Now, if the buyers pays `₹(1045 xx 108)/(1000)`
then printed price = ₹100
and if buyer pays ₹451.44, then printed price
= `₹(100 xx 451.44 xx 1000)/(1045 xx 105)`
= `(100 xx 45144 xx 1000)/(100 xx 1045 xx 108)`
= ₹400
∴ Printed price = ₹400
(ii) Now, gain of the retailer
= S.P. - C.P.
= `₹(1045)/(10) - (85)/(1)`
= `(1045 - 850)/(10)`
= `₹(195)/(10)`
∴ Gain percent
= `("Total gain" xx 100)/"C.P."`
= `(195 xx 100)/(10 xx 85)`
= `(390)/(17)`
= `22(16)/(17)%`.
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