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.
- Divide Equation 1 by 2: $3x - y = 33000$.
- Rearrange to find $y$: $y = 3x - 33000$.
- Substitute this expression for $y$ into Equation 2: $7x - 4(3x - 33000) = 66000$
- 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.
Important Questions from Ratio and Proportion (Railways)
If a : b = 3 : 2 and b : c = 3 : 2, then a : b : c = ?
If three numbers are in the ratio 5 : 6 : 8 and their sum is 3800, then the greatest number will be:
- Find the mean proportional between 7.2 and 20.
- What number will be in the place of x?
2.8 : 3.8 : : x : 5.7 - If 3A = 4B = 8C, what is A : B : C?
