The ratio of incomes of X and Y is 5 : 4 and the ratio of their expenditures is 3 : 2. If both save Rs 1000 each, find the income of X (in Rs).

The correct option is 2500.

Step-by-Step Explanation:
Let the incomes of X and Y be represented in terms of a variable $x$.
Since the ratio of their incomes is $5:4$:
Income of X = $5x$
Income of Y = $4x$

We are given that each person saves Rs 1000.
Since Expenditure = Income - Savings, we can express their expenditures as:
Expenditure of X = $5x-1000$
Expenditure of Y = $4x-1000$

The ratio of their expenditures is given as $3:2$. Therefore, we can set up the equation:

$\frac{5x-1000}{4x-1000}=\frac{3}{2}$

Now, cross-multiply to solve for $x$:

$2(5x-1000)=3(4x-1000)$

$10x-2000=12x-3000$

Rearranging the terms:

$12x-10x=3000-2000$

$2x=1000$

$x=500$

We need to find the income of X, which is $5x$:

Income of X = $5\times 500=2500$

Thus, the income of X is Rs 2500.