Step 1: Let the monthly incomes of X and Y be $4a$ and $3a$, respectively. Step 2: Let the monthly expenses of X and Y be $3b$ and $2b$, respectively. Step 3: Savings of X = Income of X - Expenses of X = $4a - 3b = 6,000$ Step 4: Savings of Y = Income of Y - Expenses of Y = $3a - 2b = 6,000$ Step 5: Solve the system of equations:

• $4a - 3b = 6,000$ → Equation 1
• $3a - 2b = 6,000$ → Equation 2 Step 6: Multiply Equation 2 by 3: $9a - 6b = 18,000$ Step 7: Multiply Equation 1 by 2: $8a - 6b = 12,000$ Step 8: Subtract the second equation from the first:
• $(9a - 6b) - (8a - 6b) = 18,000 - 12,000$
• $a = 6,000$ Step 9: Substitute $a = 6,000$ into Equation 1:
• $4(6,000) - 3b = 6,000$
• $24,000 - 3b = 6,000$
• $3b = 18,000$
• $b = 6,000$ Step 10: Total income = $4a + 3a = 7a = 7 \times 6,000 = 42,000$ Final Answer: Total monthly income = Rs. 42,000