Question

Annual expenses of A and B are in the ratio $5:3$. The saving of A and B are in the ratio $1:2$.Find the expenses of A given that the income of A is $Rs.8000$ and that of B is $Rs.9000$

• A. 3000
• B. 5000
• C. 1000
• D. 7000

Answer 1

The correct option is B 5000

Given

Income of $A$ is $8000$

Income of $B$ is $9000$

Expense Ratio is $5:3$

Let the common factor be $x$

So Expenses of $A$ are $5x$

Expenses of $B$ are $3x$

Savings Ratio is $1:2$

Let the common factor be $y$

So Savings of $A$ are $y$

Savings of $B$ are $2y$

According to Question

$5x+y=8000\cdots \left(1\right)$

$3x+2y=9000\cdots \left(2\right)$

$2\left(1\right)-\left(2\right)$

$⟹10x+2y-3x-2y=16000-9000$

$⟹7x=7000$

$⟹x=1000$

Expenses of $A$ is $5x=5\times 1000=5000$