Question

The ratio of the incomes of A and B is \(5:4\) and the ratio of their expenditures is \(3:2\). If at the end of the year, each saves ₹1600, then the income of A is

• A. ₹3400
• B. ₹3600
• C. ₹4000
• D. ₹4400

Hint:

Set up equations based on Income - Expenditure = Savings for each person.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Income = Expenditure + Savings. Let incomes be 5x and 4x, expenditures be 3y and 2y.

Step 2: Detailed Explanation:
For A: \(5x - 3y = 1600\)
For B: \(4x - 2y = 1600\)
Multiply second equation by 1.5: \(6x - 3y = 2400\)
Subtract first from this: \((6x-3y) - (5x-3y) = 2400 - 1600\) → \(x = 800\).
Income of A = \(5x = 5 \times 800 = 4000\).

Step 3: Final Answer:
₹4000