Question

The ratio of monthly incomes of A and B is 7 : 6 and the ratio of their monthly expenditures is 5 : 4. If each of them saves Rupees 600 per month, find the sum of their monthly incomes?

• A. 3600
• B. 2100
• C. 3900
• D. None of these

Hint:

When ratios of income and expenditure are given along with equal savings, always assume variables for incomes and expenditures, form two equations, and solve simultaneously.

Answer 1

The Correct Option is C

Step 1: Assume the incomes. Let the monthly incomes of A and B be \(7x\) and \(6x\) respectively. 

Step 2: Assume the expenditures. Let the monthly expenditures of A and B be \(5y\) and \(4y\) respectively. 

Step 3: Use the saving condition. Savings = Income – Expenditure. 

- For A: \(7x - 5y = 600\) 

- For B: \(6x - 4y = 600\) 

Step 4: Form simultaneous equations. \[ 7x - 5y = 600 \quad ...(1) \] \[ 6x - 4y = 600 \quad ...(2) \] 

Step 5: Simplify equations. From (2): \(6x - 4y = 600 \Rightarrow 3x - 2y = 300 \quad ...(3)\) Multiply (3) by 2: \[ 6x - 4y = 600 \] (Already the same form). Now solve (1): \[ 7x - 5y = 600 \] Multiply (3) by 5: \[ 15x - 10y = 1500 \] Multiply (1) by 2: \[ 14x - 10y = 1200 \] Subtract: \[ (15x - 10y) - (14x - 10y) = 1500 - 1200 \] \[ x = 300 \] 

Step 6: Find incomes. 

- Income of A = \(7x = 7 \times 300 = 2100\) 

- Income of B = \(6x = 6 \times 300 = 1800\) 

Step 7: Find sum. \[ \text{Total income} = 2100 + 1800 = 3900 \] 

Step 8: Final Answer. \[ \text{Sum of incomes} = 2100 + 1800 = \boxed{3900} \]