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Question
A publisher gives his distributor a discount of 30% on the printed price of the books. The distributor sells those books to a bookseller at 23% discount on the printed price and the bookseller sells these books at their printed price. Find the profit percent made by the distributor and the bookseller.
Solution
Let the printed price of the books be Rs.x
Discount given by the publisher
= 30% of Rs.x
= `(30)/(100) xx "Rs."x`
= Rs.`(30x)/(100)`
So, the distributor bought the books at Rs. x - Rs.`(30x)/(100)`
= Rs.`(70x)/(100)`
Discount given by the distributor
= Rs.23% of Rs.x
= Rs.`(23)/(100)` of Rs. x
= Rs.`(23x)/(100)`
So, the bookseller purchased the books at Rs. x - Rs.`(23x)/(100)`
= Rs.`(77x)/(100)`
Profit made by the distributor
= S.P. - C.P.
= Rs.`(77x)/(100) - "Rs."(70x)/(100)`
= Rs.`(7x)/(100)`
Profit %
= `"profit"/"C.P." xx 100`
= `((7x)/100)/((70x)/100) xx 100`
= 10%
S.P. at which the bookseller sold the books = Rs.x
So, profit
= S.P. - C.P.
= Rs. x - Rs.`(77x)/(100)`
= Rs.`(53x)/(100)`
Profit%
= `"profit"/"C.P." xx 100`
= `((23x)/100)/((77x)/100) xx 100`
= `29(67)/(77)`%
Hence, the profit% made by the distributor is 10% and that made by the bookseller is `29(67)/(77)`%.
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