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Question
A trader allows a discount of 12% on the marked price of the goods in his shop. He still makes a gross profit of 21% on the cost price. Find the profit percent he would have made, had he sold the goods at the marked price.
Solution
Let the C.P. be Rs.100.
Given that the profit% = 21% on the C.P.
Profit% = `"profit"/"C.P." xx 100`
= 21% = `"profit"/(100) xx 100`
⇒ profit = Rs.21
S.P. = C.P. + Profit
= 100 + 21
= Rs.121
Let the market price of the goods be rs. x.
Discount = 12% of M.P.
= `(12)/(100) xx x`
= Rs.`(12x)/(100)`
So, S.P. = M.P. - Discount
⇒ 121 = Rs.`(x - (12x)/100)`
⇒ x = Rs.`(121 xx 100)/(88)`
⇒ x = Rs.137.5%
If the goods were sold at the M.P., that S.P. = M.P.
So, M.P. - C.P.
= 137.7 - 100
= 37.5
= profit
Profit% = `(37.5)/(100) xx 100`
= 37.5%
Hence, the profit percent would be 37.5%.
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