The incomes of A and B are in the ratio 3 : 2 and their expenditures are in the ratio 5 : 3. If each saves Rs. 1,000 per month, what is A’s income?

Introduction / Context:
This is a paired-ratio savings problem. Define incomes and expenditures with separate multipliers and use “saving = income − expenditure.” Two linear equations arise and can be solved quickly for the income scale.

Given Data / Assumptions:

• Income ratio A : B = 3 : 2 ⇒ incomes = 3x and 2x.
• Expenditure ratio A : B = 5 : 3 ⇒ expenditures = 5y and 3y.
• Savings: 3x − 5y = 1000 and 2x − 3y = 1000.

Concept / Approach:
Solve the two simultaneous linear equations for x and y. Once x is known, A’s income is 3x. Elimination is quick by aligning one variable’s coefficients.

Step-by-Step Solution:
3x − 5y = 1000 … (1)2x − 3y = 1000 … (2)Multiply (2) by 5: 10x − 15y = 5000Multiply (1) by 3: 9x − 15y = 3000Subtract: x = 2000 ⇒ A’s income = 3x = Rs. 6000

Verification / Alternative check:
Compute y from (2): 2*2000 − 3y = 1000 ⇒ y = 1000. Expenditures become 5y = 5000 (A) and 3y = 3000 (B). Savings: 6000 − 5000 = 1000 and 4000 − 3000 = 1000, correct.

Why Other Options Are Wrong:
Other choices do not satisfy both savings equations simultaneously when checked.

Common Pitfalls:
Assuming income and expenditure share the same multiplier or directly subtracting ratios; keep separate multipliers for each ratio.

Final Answer:
Rs. 6000