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Question

# A dealer gets Rs 470 more if instead of selling a table at a loss of 10%, it is sold at a gain of 10%. Find the cost price of the table.

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Solution

## $\mathrm{Let}Rsxbethe\mathrm{CP}\mathrm{of}the\mathrm{table}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Case}\mathrm{I}:\phantom{\rule{0ex}{0ex}}\mathrm{Loss}\mathrm{percentage}=10%\phantom{\rule{0ex}{0ex}}⇒\mathrm{Loss}%=\left(\frac{\mathrm{loss}}{\mathrm{CP}}×100\right)%\phantom{\rule{0ex}{0ex}}⇒10=\frac{\mathrm{loss}}{x}×100\phantom{\rule{0ex}{0ex}}⇒\frac{\mathrm{Loss}}{x}=\frac{1}{10}\phantom{\rule{0ex}{0ex}}⇒\mathrm{Loss}=\mathrm{Rs}\frac{x}{10}\phantom{\rule{0ex}{0ex}}\mathrm{Suppose}\mathrm{that}{\mathrm{SP}}_{1}\mathrm{is}\mathrm{the}\mathrm{selling}\mathrm{price}\mathrm{when}\mathrm{he}\mathrm{incurs}\mathrm{a}\mathrm{loss}\mathrm{of}10%.\phantom{\rule{0ex}{0ex}}\mathrm{Loss}=\mathrm{Rs}\frac{\mathrm{x}}{10}\phantom{\rule{0ex}{0ex}}⇒\mathrm{CP}-{\mathrm{SP}}_{1}=\frac{x}{10}\phantom{\rule{0ex}{0ex}}⇒{\mathrm{SP}}_{1}=x-\frac{x}{10}\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}\frac{9x}{10}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Case}\mathrm{II}:\phantom{\rule{0ex}{0ex}}\mathrm{Gain}\mathrm{percentage}=10%\phantom{\rule{0ex}{0ex}}⇒\mathrm{Gain}%=\left(\frac{\mathrm{gain}}{\mathrm{CP}}×100\right)%\phantom{\rule{0ex}{0ex}}⇒10=\frac{\mathrm{gain}}{x}×100\phantom{\rule{0ex}{0ex}}⇒\frac{\mathrm{Gain}}{x}=\frac{1}{10}\phantom{\rule{0ex}{0ex}}⇒\mathrm{Gain}=\mathrm{Rs}\frac{x}{10}\phantom{\rule{0ex}{0ex}}\mathrm{Suppose}\mathrm{that}{\mathrm{SP}}_{2}\mathrm{is}\mathrm{the}\mathrm{selling}\mathrm{price}\mathrm{when}\mathrm{he}\mathrm{makes}\mathrm{gain}\mathrm{of}10%.\phantom{\rule{0ex}{0ex}}\mathrm{Now},{\mathrm{SP}}_{2}=\mathrm{gain}+\mathrm{CP}\phantom{\rule{0ex}{0ex}}⇒{\mathrm{SP}}_{2}=\frac{x}{10}+x\phantom{\rule{0ex}{0ex}}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}=\mathrm{Rs}\frac{11\mathrm{x}}{10}\phantom{\rule{0ex}{0ex}}\mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{differnce}\mathrm{between}\mathrm{the}\mathrm{selling}\mathrm{prices}\mathrm{in}\mathrm{both}\mathrm{the}\mathrm{case}\mathrm{is}\mathrm{Rs}470.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Now},{\mathrm{SP}}_{2}-{\mathrm{SP}}_{1}=470\phantom{\rule{0ex}{0ex}}⇒\frac{11x}{10}-\frac{9x}{10}=470\phantom{\rule{0ex}{0ex}}⇒\frac{2x}{10}=470\phantom{\rule{0ex}{0ex}}⇒2x\mathit{=}4700\phantom{\rule{0ex}{0ex}}⇒x=2350\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},\mathrm{the}\mathrm{CP}\mathrm{of}\mathrm{the}\mathrm{chair}\mathrm{is}\mathrm{Rs}2350.$

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