Question

The ratio of income of two persons is $9:7$ and the ratio of their expenditure is $4:3$. If each of them saves Rs. $200$ per month, find their monthly income.

• A. Rs. $2200$, Rs. $1400$
• B. Rs. $2100$, Rs. $1400$
• C. Rs. $1800$, Rs. $1400$
• D. Rs. $1900$, Rs. $1400$

Answer 1

The correct option is C Rs. $1800$, Rs. $1400$

The ratio of income of two persons is $9:7$ and the ratio of their expenditure is $4:3$. If each of them saves Rs. $200$ per month.
Let income of first person be Rs. $9x$ and of second person be Rs. $7x$, then their expenditure are Rs $4y$ and Rs $3y$ respectively.
For first person, For second person,
$9x-4y=200$ ....$\left(1\right)$ $7x-3y=200$ ...$\left(2\right)$
Multiply equation $\left(1\right)$ by $3$ and equation $\left(2\right)$ by $4$, then subtract $\left(2\right)$ from $\left(1\right)$
$27x-12y=600$
$28x-12y=800$
Subtracting,
$-x+0=-200$
$\Rightarrow x=200$
put it in equation $\left(1\right)$
$9\times 200-4y=200$
$y=400$
Income of first person $=$ Rs. $9\times 200=$ Rs. $1800$
and of second person is $=$ Rs. $7\times 200=$ Rs. $1400$