The incomes of X and Y are in the ratio of 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves Rs 1250, find their incomes.

Let the income of  be Rs and the income of  be Rs.further let the expenditure of  be  and the expenditure of be  respectively then,

Saving of $x=8 x-19 y$

Saving of $Y=7 x-16 y$

$8 x-19 y=1250$

$7 x-16 y=1250$

$8 x-19 y-1250=0 \cdots(i)$

$7 x-16 y-1250=0 \cdots(i i)$

Solving equation  and  by cross- multiplication, we have

$\frac{x}{(-19 \times-1250)-(-16 \times-1250)}=\frac{-y}{(8 \times-1250)-(7 \times-1250)}=\frac{1}{(8 \times-16)-(7 \times-19)}$

$\frac{x}{23750-20000}=\frac{-y}{-10000+8750}=\frac{1}{-128+133}$

$\frac{x}{3750}=\frac{y}{1250}=\frac{1}{5}$

$x=\frac{3750}{5}$

The monthly income of $X=8 x$

$$

\begin{aligned}

&=8 \times 750 \\

&=6000

\end{aligned}

$$

The monthly income of $Y=7 x$

$$

\begin{aligned}

&=7 \times 750 \\

&=5250

\end{aligned}

$$

Hence the monthly income of $X$ is Rs $R s .6000$

The monthly income of $Y$ is Rs Rs. 5250