Question

The incomes of A and B are in the ratio $3:2$ and their expenditures are in the ratio $5:3$.If each saves Rs.$1000$ , then A's income is ______.

• A. Rs.$3000$
• B. Rs.$4000$
• C. Rs.$6000$
• D. Rs.$9000$

Answer 1

The correct option is C Rs.$6000$

$\Rightarrow$ Let income of A and B be $3x$ and $2x$ respectively. Also, their expenditure is $5y$ and $3y.$

$\Rightarrow$ Now, according to question,

$\Rightarrow$ $3x-5y=1000$ ---- ( 1 )

$\Rightarrow$ $2x-3y=1000$ ----- ( 2 )

$\Rightarrow$ Now, multiplying equation ( 1 ) by 3 and ( 2) by 5.

$\Rightarrow$ $9x-15y=3000$ ---- ( 3 )

$\Rightarrow$ $10x-15y=5000$ ----- ( 4 )

$\Rightarrow$ $x=2000$ [Subtraction equation ( 3 ) from equation ( 4 ) ]

$\Rightarrow$ Then, income of $A$ = $3x=Rs.(3\times 2000)=Rs,.6000.$