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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.
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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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