Question

The monthly income of $A$ and $B$ are in the ratio of $5:4$ and their monthly expenditures are in the ratio of $7:5$. If each saves Rs. $3,000$ per month, find the monthly income of each.

Answer 1

We know that $Income=Expenditure+Savings$

Let $5x,4x$ be the incomes of $A$ and $B$ respectively.

and $7y,5y$ be the expenditures of $A$ and $B$ respectively.

$\Rightarrow 5x=7y+3000$ or $5x-7y=3000$ .......$\left(1\right)$ of $A$

$\Rightarrow 4x=5y+3000$ or $4x-5y=3000$ .......$\left(2\right)$ of $B$

Eqn$\left(1\right)-\left(2\right)$ gievs,

$5x-7y-4x+5y=3000-3000$

$x-2y=0$ or $x=2y$

Substitute $x=2y$ in $\left(1\right)$ we get

$5\times 2y-7y=3000$

$\Rightarrow 10y-7y=3000$

$\Rightarrow 3y=3000$ or $y=1000$

Put $y=1000$ in $x=2y$ we get $x=2\times 1000=2000$

Hence Monthly income of $A$ is $5x=5\times 2000=Rs.10,000$ and that of $B$ is $4x=4\times 2000=Rs.8,000$