Question

The ratio of income of two persons is $9:7$ and the ratio of their expenditure is $4:3$. If each of them manages to save Rs. $2000$ per month, find their monthly income.

• A. $Rs.18,000,Rs.14,000$
• B. $Rs.1,000,Rs.14,000$
• C. $Rs.18,000,Rs.1,000$
• D. None of these

Answer 1

Answer: (A)

$Rs.18,000,Rs.14,000$

Let their salaries be $9x$ and $7x$.

Let their expenditure be $4y$ and $3y$.

According to the question,

$9x-4y=2000$ $—\left(1\right)$

$7x-3y=2000$ $—\left(2\right)$

From $\left(1\right)$

$x=\frac{2000+4y}{9}$ $—\left(3\right)$

On putting $x$ in $\left(2\right)$, we get

$7\times \frac{(2000+4y)}{9}-3y=2000$

$\frac{(14000+28y)}{9}-3y=2000$

$\frac{14000+28y-27y}{9}=2000$

$14000+y=18000$

$y=4000$

Now, put $y$ in (3)

$x=\frac{2000+4\times 4000}{9}$

$x=\frac{2000+16000}{9}$

$x=\frac{18000}{9}=2000$

So,

Salary of first person $=9\times 2000=Rs.18000$

Salary of second person $=7\times 2000=Rs.14000$

Hence, this is the answer.