The monthly incomes of X and Y are in the ratio of 4 : 3 and their monthly expenses are in the ratio of 3 : 2. However, each saves ₹6,000 per month. What is their total monthly income?

The correct option is ₹42,000.

Step-by-Step Explanation:

Step 1: Express the monthly incomes in terms of a variable
The monthly incomes of X and Y are given in the ratio of $4:3$.
Let the monthly income of X be $4x$ and the monthly income of Y be $3x$.

Step 2: Express their monthly expenses
We know the basic financial relationship:
$\text{Expense}=\text{Income}-\text{Savings}$
Since each person saves ₹6,000 per month:
Monthly expense of X = $4x-6000$
Monthly expense of Y = $3x-6000$

Step 3: Formulate the ratio equation for expenses
The ratio of their monthly expenses is given as $3:2$. Setting up the ratio:

$\frac{4x-6000}{3x-6000}=\frac{3}{2}$

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

$2\times (4x-6000)=3\times (3x-6000)$

Expand both sides:

$8x-12000=9x-18000$

Rearrange the terms to isolate $x$:

$9x-8x=18000-12000$

$x=6000$

Step 5: Calculate their total monthly income
Total monthly income = Income of X + Income of Y

$\text{Total Income}=4x+3x=7x$

Substitute $x=6000$:

$\text{Total Income}=7\times 6000=42000$

Therefore, their total monthly income is ₹42,000.