# 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.

Question:

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.

Solution:

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