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Question

# By selling a book for Rs 258, a bookseller gains 20%. For how much should he sell it to gain 30%?

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Solution

## $\phantom{\rule{0ex}{0ex}}\mathrm{Selling}\mathrm{price}\mathrm{of}the\mathrm{book}=\mathrm{Rs}.258\phantom{\rule{0ex}{0ex}}\mathrm{Gain}%=20%\phantom{\rule{0ex}{0ex}}\mathrm{Since},\mathrm{C}.\mathrm{P}=\left[\frac{100}{\left(100+\mathrm{Gain}%\right)}×S.P\right]\phantom{\rule{0ex}{0ex}}=\left[\frac{100}{\left(100+20\right)}×258\right]\phantom{\rule{0ex}{0ex}}=\frac{25800}{120}\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.215\phantom{\rule{0ex}{0ex}}\mathrm{Let}\mathrm{the}\mathrm{bookseller}sells\mathrm{it}for\mathrm{Rs}.x\phantom{\rule{0ex}{0ex}}So,S.P=\left[\frac{\left(100+\mathrm{Gain}%\right)}{100}×C.P\right]\phantom{\rule{0ex}{0ex}}x=\frac{100+30}{100}×215\phantom{\rule{0ex}{0ex}}=\frac{130×215}{100}\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.279.50\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},the\mathrm{bookseller}\mathrm{must}\mathrm{sell}thebookat\mathrm{Rs}279.50\mathrm{to}make30%profit.$

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