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: Let incomes of A and B be \(7x\) and \(6x\), and expenditures be \(5y\) and \(4y\). Since both save Rupees 600, \(7x-5y=600\) and \(6x-4y=600\).

Step 2: Eliminate \(x\) first. From the second equation, \(x=100+\dfrac{2y}{3}\). Substitute into the first: \(7\left(100+\dfrac{2y}{3}\right)-5y=600\), which simplifies to \(700+\dfrac{14y}{3}-5y=600\), so \(-\dfrac{y}{3}=-100\), giving \(y=300\).

Step 3: Put \(y=300\) back into \(6x-4(300)=600\), so \(6x=1800\) and \(x=300\).

Step 4: Incomes are \(7x=2100\) and \(6x=1800\), so their sum is \[ \boxed{3900} \]