Income Ratio Setup

Let Tushar's monthly income be $6x$ and Salil's monthly income be $7x$, based on the given ratio $6:7$.

Expenditure and Savings Equations

Both friends save ₹66,000 monthly. The ratio of their monthly expenditures is $2:4$.

Let Tushar's monthly expenditure be $2y$ and Salil's monthly expenditure be $4y$.

The relationship is Income - Expenditure = Savings.

• For Tushar: $6x - 2y = 66000$ (Equation 1)
• For Salil: $7x - 4y = 66000$ (Equation 2)

Solving for Monthly Income

We solve the system of linear equations for $x$ to find the incomes.

1. Divide Equation 1 by 2: $3x - y = 33000$.
2. Rearrange to find $y$: $y = 3x - 33000$.
3. Substitute this expression for $y$ into Equation 2: $7x - 4(3x - 33000) = 66000$
4. Simplify and solve for $x$: $7x - 12x + 132000 = 66000$ $-5x = 66000 - 132000$ $-5x = -66000$ $x = \frac{-66000}{-5}$ $x = 13200$

Tushar's Monthly Income

Tushar's monthly income is $6x$. Substitute the value of $x$:

Tushar's Income $= 6 \times 13200 = 79200$.

The monthly income of Tushar is ₹79,200.