Question

The annual incomes of A and B are in the ratio 3 : 4 and their annual expenditures are in the ratio 5 : 7. If each saves Rs. 5, 000 then, find their annual incomes.

• A. A = Rs. 22,000 and B = Rs. 30,000
• B. A = Rs. 30,000 and B = Rs. 40,000
• C. A = Rs. 50,000 and B = Rs. 70,000
• D. A = Rs. 40,000 and B = Rs. 20,000

Answer 1

Answer: (B)

A = Rs. 30,000 and B = Rs. 40,000

Let the annual incomes of A and B be $3x$ and $4x$
And the annual expenditures of A and B be $5y$ and $7y$
Since each of them saves $Rs5000$.
$3x-5y=5000$ ----- (1)
$4x-7y=5000$ ---- (2)

Multiplying equation $\left(1\right)$ with $4$ we get, $12x-20y=20000$ ----- equation $\left(3\right)$

Multiplying equation $\left(2\right)$ with $3$ we get, $12x-21y=15000$ ----- equation $\left(4\right)$

Subtracting equation $\left(4\right)$ from $\left(3\right)$, we get $y=5000$

Substituting $y=5000$ in the equation $\left(1\right)$, we get $3x-5\left(5000\right)=5000=x=10000$

Hence,, annual income of A $=3x=$ Rs $30000$ and of B $=4x=$ Rs $40000$