# The ratio of expenditure of A,B and C is 16:12:9.Their total income is Rs.1530.Find the shares of B's income if they save 20%,25% and 40% of the income.

$Incomeiseithersavedorspent.\phantom{\rule{0ex}{0ex}}Thus,Income=Expenditure+Saving\phantom{\rule{0ex}{0ex}}\Rightarrow Income-Saving=Expenditure\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}LettheincomesofA,BandCbex,yandzrespectively.\phantom{\rule{0ex}{0ex}}Then,x+y+z=Rs.1,530\phantom{\rule{0ex}{0ex}}Now,A,BandCsave20\%,25\%and40\%oftheirincomesrespectively.\phantom{\rule{0ex}{0ex}}Therefore,Asaves=20\%ofx=\frac{20x}{100}=\frac{x}{5};Bsaves=25\%ofy=\frac{25y}{100}=\frac{y}{4}andCsaves=40\%ofz=\frac{40z}{100}=\frac{2z}{5}\phantom{\rule{0ex}{0ex}}Hence,A\text{'}sexpenditure=x-\frac{x}{5}=\frac{4x}{5};B\text{'}sexpenditure=y-\frac{y}{4}=\frac{3y}{4}andC\text{'}sexpenditure=z-\frac{2z}{5}=\frac{3z}{5}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}ExpenditureofA:B:C=16:12:9\phantom{\rule{0ex}{0ex}}LettheexpendituresofA,BandCbe16k,12kand9krespectively.\phantom{\rule{0ex}{0ex}}So,\frac{4x}{5}=16k,\frac{3y}{4}=12kand\frac{3z}{5}=9k\phantom{\rule{0ex}{0ex}}\Rightarrow x=20k,y=16kandz=15k.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Now,x+y+z=1530\phantom{\rule{0ex}{0ex}}\Rightarrow 20k+16k+15k=1530\phantom{\rule{0ex}{0ex}}\Rightarrow 51k=1530\phantom{\rule{0ex}{0ex}}\Rightarrow k=30\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Thus,B\text{'}sincome=y=16k=16\times 30=Rs.480$

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