Income and Expenditure Ratio Calculation

This section details the calculation to find the incomes of Barun and Anil based on their income ratio, expenditure ratio, and savings.

Setting Up the Ratios

Let the common multiplier for Barun and Anil's incomes be $x$, and the common multiplier for their expenditures be $y$.

• Barun's Income: $I_B = 12x$
• Anil's Income: $I_A = 13x$
• Barun's Expenditure: $E_B = 10y$
• Anil's Expenditure: $E_A = 13y$

Savings are defined as Income - Expenditure ($S = I - E$).

Given savings:

• Barun's Savings: $S_B = ₹2100$
• Anil's Savings: $S_A = ₹1300$

Formulating Equations

Using the savings formula, we can set up two equations:

• For Barun: $12x - 10y = 2100$ (Equation 1)
• For Anil: $13x - 13y = 1300$ (Equation 2)

Solving for Incomes

1. Simplify Equation 2 by dividing by 13: $x - y = 100$ Rearrange to find $y$: $y = x - 100$
2. Substitute this expression for $y$ into Equation 1: $12x - 10(x - 100) = 2100$
3. Solve the equation for $x$: $12x - 10x + 1000 = 2100$ $2x = 2100 - 1000$ $2x = 1100$ $x = \frac{1100}{2}$ $x = 550$
4. Calculate the respective incomes using the value of $x$: Barun's Income $= 12x = 12 \times 550 = ₹6600$ Anil's Income $= 13x = 13 \times 550 = ₹7150$

Thus, the incomes of Barun and Anil are $₹6600$ and $₹7150$, respectively.