Question

The monthly earning and expenditures of A and B are in the ratio 5 : 7 and 2 : 1 respectively .Find A's earning per month if the monthly savings of B is twice that of A. also given that A saved rupees 578 every month. ​

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{Income \ of \ A \ is \ Rs \ 1348.9}$

$\sf\orange{Given:}$

$\sf{\implies{The \ monthly \ earning \ of \ A \ and \ B}}$

$\sf{are \ in \ ratio \ of \ 5:7 \ and \ expenditures}$

$\sf{is \ in \ ratio \ of \ 2:1.}$

$\sf{\implies{Saving \ of \ A=Rs \ 578}}$

$\sf{\implies{Saving \ of \ B=2\times \ Saving \ of \ A}}$

$\sf{i.e \ Saving \ of \ B=2(578)=Rs \ 1156}$

$\sf\pink{To \ find:}$

$\sf{Earning \ of \ A}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ income \ of \ A \ and \ B \ be \ in \ ratio}$

$\sf{5x:7x}$

$\sf{Let \ expenditure \ of \ A \ and \ B \ in \ ratio}$

$\sf{2y:1y}$

$\boxed{\sf{Income \ - \ Expenditure=Saving}}$

$\sf{\therefore{For \ A,}}$

$\sf{5x-2y=578...(1)}$

$\sf{\therefore{For \ B,}}$

$\sf{7x-y=1156...(2)}$

$\sf{Multiply \ equation \ (2) \ by \ 2 \ we \ get,}$

$\sf{14x-2y=2312...(3)}$

$\sf{Subtract \ equation (1) \ from \ equation (3)}$

$\sf{14x-2y=2312}$

$\sf{-}$

$\sf{5x-2y=578}$

______________________

$\sf{9x=1734}$

$\sf{x=\frac{1734}{9}}$

$\sf{x=192.7 \ (approx)}$

$\sf{\therefore{Income \ of \ A=7(192.7)}}$

$\sf{\implies{Rs \ 1348.9}}$

$\sf\purple{\tt{\therefore{Income \ of \ A \ is \ Rs \ 1348.9}}}$

Answer 2

★$\color{darkblue}\underline{\underline{\sf Question:}}$

$\rm{The \ monthly \ earning \ and \ expenditures \ A}$

$\rm{and \ B \ are \ in \ the \ ratio \ 5 \ : \ 7 \ and \ 2 \ : \ 1 }$

$\rm{ respectively . \ Find \ A's \ earning \ per \ month }$

$\rm{if \ the \ monthly \ savings \ of \ B \ is \ twice \ that }$

$\rm{of \ A. \ Also \ given \ that \ A \ saved \ rupees }$

$\rm{578 \ every \ month}$

_________________________________________

★$\color{green}\underline{\underline{\sf Answer:}}$

$\rm\purple{Income \ of \ A \ is \ Rs \ 1348.9}$

_________________________________________

$\sf\large\underline\red{Given:}$

$\rm{The \ monthly \ earning \ of \ A \ and \ B}$

$\rm{are \ in \ ratio \ of \ 5:7 \ and \ expenditures}$

$\rm{is \ in \ ratio \ of \ 2:1.}$

$\rm{Saving \ of \ A=Rs \ 578}$

$\rm{Saving \ of \ B=2\times \ Saving \ of \ A}$

$\rm{i.e \ Saving \ of \ B=2(578)=Rs \ 1156}$

_________________________________________

$\sf\large\underline\orange{To \ Find:}$

$\rm{Earning \ of \ A}$

_________________________________________

★$\color{pink}\underline{\underline{\sf Answer:}}$

$\rm{Let \ income \ of \ A \ and \ B \ be \ in \ ratio}$

$\rm{5x:7x}$

$\rm{Let \ expenditure \ of \ A \ and \ B \ in \ ratio}$

$\rm{2y:1y}$

$\star{\bf{Income \ - \ Expenditure=Saving}}$

$\rm{\implies{For \ A,}}$

$\rm{5x-2y=578....................[a]}$

$\rm{\implies{For \ B,}}$

$\rm{7x-y=1156......................[b]}$

$\rm{Multiply \ equation \ [b] \ by \ 2 \ we \ get,}$

$\rm{14x-2y=2312................[c]}$

$\rm{Subtract \ equation \ [b] \ from \ equation [c]}$

$\rm{9x=1734}$

$\rm{x=\frac{1734}{9}}$

$\rm{x=192.7 \ (approximate \ value)}$

$\sf{\implies{Income \ of \ A=7(192.7)}}$

$\rm{Rs \ 1348.9}$

$\sf\orange{\bf{\implies{Income \ of \ A \ is \ Rs \ 1348.9}}}$