# 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

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