    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?

Open in App
Solution

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