Question

The ratio of the incomes of $A$ and $B$ is $5:4$ and the ratio of their expenditures is $3:2$. If at the end of the year, each saves $Rs.1600$, then the income of $A$ is:

• A. $Rs.3400$
• B. $Rs.3600$
• C. $Rs.4000$
• D. $Rs.4400$

Answer 1

The correct option is C $Rs.4000$

Let their income be $x$ and expenditure be $y$.

$A^{\prime }s$ income $=5x$

$B^{\prime }s$ income $=4x$

$A^{\prime }s$ expenditure $=3y$

$B^{\prime }s$ expenditure $=2y$

Save money $=Rs.1600$

$\Rightarrow$ Income - expenditure = saves

$\Rightarrow$ $5x-3y=1600$ ---- ( 1 )

$\Rightarrow$ $4x-2y=1600$ --- ( 2 )

Multiply equation ( 1 ) by $2$ and equation ( 2 ) by $3$, we get,

$\Rightarrow$ $10x-6y=3200$ ---- ( 3 )

$\Rightarrow$ $12x-6y=4800$ ---- ( 4 )

By subtracting ( 4 ) from ( 1 ) we get,

$\Rightarrow$ $x=800$

$\Rightarrow$ Income of $A=5x=5\times 800=Rs.4000$