Calculating Vipul's Monthly Income

Let the monthly incomes of Vipul and Vijay be $6x$ and $7x$ respectively, based on the given ratio 6 : 7.

Both save ₹66,000 per month.

The ratio of their monthly expenditures is 1 : 3. Let Vipul's expenditure be $y$ and Vijay's expenditure be $3y$.

We know that Income = Expenditure + Savings.

For Vipul:

Vipul's Income - Vipul's Expenditure = Vipul's Savings

$6x - y = 66000 \quad \cdots (1)$

For Vijay:

Vijay's Income - Vijay's Expenditure = Vijay's Savings

$7x - 3y = 66000 \quad \cdots (2)$

Solving the Equations

To solve these equations, we can eliminate one variable. Multiply Equation (1) by 3:

$3 \times (6x - y) = 3 \times 66000$

$18x - 3y = 198000 \quad \cdots (3)$

Now, subtract Equation (2) from Equation (3):

$(18x - 3y) - (7x - 3y) = 198000 - 66000$

$18x - 3y - 7x + 3y = 132000$

$11x = 132000$

Solve for $x$:

$x = \frac{132000}{11}$

$x = 12000$

Determining Vipul's Income

Vipul's monthly income is represented by $6x$. Substitute the value of $x$:

Vipul's Income $= 6 \times 12000$

Vipul's Income $= 72000$

Therefore, Vipul's monthly income is ₹72,000.