Income–expenditure–savings with ratios: The ratio of incomes of two persons is 8 : 5 and the ratio of their expenditures is 2 : 1. Each saves ₹1000 per month. What is the difference between their monthly incomes?

Introduction / Context:
This problem links income, expenditure, and savings with given ratios. Modeling incomes and expenditures via proportional multipliers and equating savings allows us to compute the exact monthly incomes and hence their difference.

Given Data / Assumptions:

• Income ratio = 8 : 5 ⇒ I1 = 8k, I2 = 5k.
• Expenditure ratio = 2 : 1 ⇒ E1 = 2t, E2 = 1t.
• Savings: I1 − E1 = 1000 and I2 − E2 = 1000.

Concept / Approach:
Set up the two savings equations and solve for k and t. Then compute I1 and I2 explicitly and subtract to find the difference. This approach preserves the given ratios without assuming the same multiplier for income and expenditure ratios.

Step-by-Step Solution:

Verification / Alternative check:
E1 = 2t = 2(5k − 1000) = 2(1500) = 3000; E2 = t = 1500. Savings: 4000 − 3000 = 1000; 2500 − 1500 = 1000. Checks out.

Why Other Options Are Wrong:
₹2500, ₹1000, ₹700, ₹2000 do not equal the computed difference consistent with both ratios and equal savings.

Common Pitfalls:
Assuming the same multiplier for income and expenditure ratios or forgetting to impose the two separate savings conditions leads to incorrect k and t values.

Final Answer:
₹ 1,500