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 answer is 2500.

Let us solve this problem step-by-step using algebra.

Step 1: Express the incomes of X and Y using a variable.
The ratio of incomes of X and Y is given as 5 : 4.
Let the common ratio multiplier for their incomes be $x$.
Therefore:

Income of X = $5x$
Income of Y = $4x$

Step 2: Relate Income, Expenditure, and Savings.
We know the basic formula for savings:

Savings = Income - Expenditure

This can also be rewritten to express Expenditure in terms of Income and Savings:

Expenditure = Income - Savings

Given that both X and Y save Rs 1000 each:

Expenditure of X = $5x-1000$
Expenditure of Y = $4x-1000$

Step 3: Set up the equation using the ratio of expenditures.
The ratio of their expenditures is given as 3 : 2.
Setting up the ratio equation:

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

Step 4: Solve for $x$.
Cross-multiply to clear the fractions:

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

Expand both sides of the equation:

$10x-2000=12x-3000$

Rearrange the terms to solve for $x$:

$3000-2000=12x-10x$

$1000=2x$

$x=500$

Step 5: Calculate the income of X.
The income of X was defined as $5x$. Substituting the value of $x=500$:

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

Thus, the income of X is Rs 2500.