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Question
A trader allows a discount of 15% on the marked price of the goods in his shop. However, he still makes a gross profit of 36% 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%
= 36% on the C.P.
Profit%
= `"profit"/"C.P." xx 100`
⇒ 36% = `"profit"/(100) xx 100`
⇒ profit = Rs.36
S.P. = C.P. + Profit
= 100 + 36
= Rs.136
Let the marked price of the goods be Rs. x.
Discount = 15% of M.P.
= `(15)/(100) xx x`
= Rs.`(15x)/(100)`
So, S.P. = M.P. - Discount
⇒ 136 = Rs.`(x - (15x)/100)`
⇒ x = Rs.`(136 xx 100)/(85)`
⇒ x = Rs.160%
If the goods were sold at the M.P., that S.P. = M.P.
So, M.P. - C.P.
= 160 - 100
= 60
= profit
Profit%
= `(60)/(100) xx 100`
= 60%
Hence, the profit percent would be 60%.
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