 # The incomes of X and Y are in the ratio of 8 : 7 and their expenditures are in the ratio 19 : 16. `
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 $X$ be Rs $8 x$ and the income of $Y$ be Rs $7 x$.further let the expenditure of $X$ be $19 y$ and the expenditure of $Y$ be $16 y$ 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 $(i)$ and $(i i)$ 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 $X=8 x$

$=8 \times 750$

$=6000$

The monthly income of $Y=7 x$

$=7 \times 750$

$=5250$

Hence the monthly income of $X$ is Rs Rs, 6000

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