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Question

# (ix) A man gets Rs. 100 per day if he works, but he is fined by Rs 10 per day if he is absent. In the whole month of April he received Rs 1900 only. How many days did he work?

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Solution

## $\text{Suppose},\mathrm{the}\mathrm{man}\mathrm{works}\mathrm{for}xdays\mathrm{and}\mathrm{he}\mathrm{was}\mathrm{absent}\mathrm{for}y\mathrm{days}.\phantom{\rule{0ex}{0ex}}\mathrm{Money}\mathrm{he}\mathrm{gets}\mathrm{for}x\mathrm{days}=\mathrm{Rs}100x\phantom{\rule{0ex}{0ex}}\mathrm{Money}\mathrm{he}\mathrm{would}\mathrm{be}\mathrm{fined}\mathrm{for}y\mathrm{days}=\mathrm{Rs}10y\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},\mathrm{he}\mathrm{would}\mathrm{get}=\mathrm{Rs}\left(100x-10y\right)\phantom{\rule{0ex}{0ex}}\mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question},\phantom{\rule{0ex}{0ex}}100x-10y=1900\phantom{\rule{0ex}{0ex}}⇒10x-y=190...\left(1\right)\phantom{\rule{0ex}{0ex}}\mathrm{Days}\mathrm{in}\text{A}\mathrm{pril}=30\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},x+y=30\phantom{\rule{0ex}{0ex}}⇒x=30-y....\left(2\right)\phantom{\rule{0ex}{0ex}}\mathrm{Substituting}\mathrm{eq}\left(2\right)\mathrm{in}\mathrm{eq}\left(1\right),\phantom{\rule{0ex}{0ex}}10×\left(30-y\right)-y=190\phantom{\rule{0ex}{0ex}}⇒300-10y-y=190\phantom{\rule{0ex}{0ex}}⇒11y=110\phantom{\rule{0ex}{0ex}}⇒y=10\phantom{\rule{0ex}{0ex}}\mathrm{Substituting}y=10\mathrm{in}\mathrm{eq}\left(2\right),\phantom{\rule{0ex}{0ex}}x=30-10\phantom{\rule{0ex}{0ex}}⇒x=20\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},\text{the}\mathrm{man}\mathrm{works}\mathrm{for}20\mathrm{days}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

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