Question
The monthly incomes of Aryan and Babbar are in the ratio \(3:4\) and their expenditures are in the ratio \(5:7\). Each saves ₹15000 per month. Find their monthly incomes using matrix method.
Solution
Step 1: Assume
\[ \text{Income} = 3x,\ 4x \] \[ \text{Expenditure} = 5y,\ 7y \]Step 2: Savings Equation
\[ 3x – 5y = 15000 \] \[ 4x – 7y = 15000 \]Step 3: Matrix Form
\[ \begin{bmatrix} 3 & -5 \\ 4 & -7 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 15000 \\ 15000 \end{bmatrix} \]Step 4: Solve
From equations: \[ x = 30000,\quad y = 15000 \]Step 5: Income
\[ \text{Aryan} = 3x = 90000 \] \[ \text{Babbar} = 4x = 120000 \]Final Answer
Aryan’s income = ₹90000
Babbar’s income = ₹120000
Value Reflected
✔ Importance of saving money
✔ Financial planning and discipline
✔ Balanced income and expenditure
✔ Smart budgeting leads to stability