Question

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

Answer 1

Let the income of first-person be Rs $9x$ and the income of the second person be Rs. $7x$. Further, let the expenditures of the first and second person be $4y$ and $3y$ respectively. Then,

Saving of first-person $=9x-4y$
Saving of second person $=7x-3y$

$\therefore 9x-4y=200\Rightarrow 9x-4y-200=0$ (i)
and, $7x-3y-200\Rightarrow 7x-3y-200=0$ .(ii)

Solving equation (i) and (ii) by cross-multiplication, we have

$\frac{x}{(-4\times -200)-(-3\times -200)}=\frac{-y}{(-200\times -9)-(-200\times -7)}=\frac{1}{(9\times -3)-(7\times -4)}$

$\frac{x}{800-600}=\frac{-y}{-1800+1400}=\frac{1}{-27+28}$

$\Rightarrow x=200$ and $y=400$

Thus, monthly income of first person $=$Rs. $9x=$ Rs. $(9\times 200)=$ Rs. $1800$
and, monthly income of second person $=$Rs. $7x=$Rs. $(7\times 200)=$Rs. $1400$.