Question

The monthly income of $A$ and $B$ are in the ratio of $4:3$ and their monthly expenditures are in the ratio of $13:9$, If each saves Rs. $1,500$ per month, find the monthly income of each.

Answer 1

Let monthly incomes of A and B be $x\&y$

Given $\frac{x}{y}=\frac{4}{3}\Rightarrow x=\frac{4y}{3}$

Income $=expenditure+savings$

Let their expenditures be A and B

$x=A+1500y=B+1500A=x-1500B=y-1500$

Given $\frac{A}{B}=\frac{13}{9}\frac{x-1500}{y-1500}=\frac{13}{9}\frac{\frac{4y}{3}-1500}{y-1500}=\frac{13}{9}\frac{4y-4500}{3(y-1500)}=\frac{13}{9}3(4y-4500)=13(y-1500)12y-13500=13y-19500y=19500-13500=6000x=\frac{4\times 4}{3}=\frac{4\times 6000}{3}4\times 2000=8000$

$\therefore$ Monthly incomes of A and B are $8000\&6000$