The incomes of Pavan and Amar are in the ratio 4 : 3, and their expenditures are in the ratio 3 : 2. If each of them saves exactly Rs. 1889 per month, what is Pavan's monthly income?

Introduction / Context:
This is a classic income–expenditure–savings problem involving ratios. We are given the ratio of incomes, the ratio of expenditures, and the fact that both people save the same fixed amount every month. Using these relationships, we must determine the actual income of Pavan. Such problems test the ability to translate word statements into algebraic equations and solve simultaneous equations efficiently.

Given Data / Assumptions:
• Income ratio (Pavan : Amar) = 4 : 3. • Expenditure ratio (Pavan : Amar) = 3 : 2. • Monthly saving of each person = Rs. 1889. • Savings = Income − Expenditure.

Concept / Approach:
We represent incomes and expenditures in terms of unknown variables that respect the given ratios. Let incomes be 4x and 3x, and expenditures be 3y and 2y for Pavan and Amar respectively. The equal savings condition gives two equations: 4x − 3y = 1889 and 3x − 2y = 1889. Solving this linear system yields x and y. Pavan's income is then 4x.

Step-by-Step Solution:
Step 1: Let Pavan's income = 4x and Amar's income = 3x. Step 2: Let Pavan's expenditure = 3y and Amar's expenditure = 2y. Step 3: Savings of Pavan = 4x − 3y = 1889. Step 4: Savings of Amar = 3x − 2y = 1889. Step 5: Subtract the second equation from the first: (4x − 3y) − (3x − 2y) = 1889 − 1889. Step 6: Simplify: 4x − 3y − 3x + 2y = 0 ⇒ x − y = 0 ⇒ x = y. Step 7: Substitute x = y into 3x − 2y = 1889, giving 3x − 2x = 1889 ⇒ x = 1889. Step 8: Pavan's income = 4x = 4 * 1889. Step 9: Compute 4 * 1889 = (4 * 1800) + (4 * 89) = 7200 + 356 = 7556.

Verification / Alternative check:
Check Amar's values: Amar's income = 3x = 3 * 1889 = 5667. Amar's expenditure = 2y = 2 * 1889 = 3778, so savings = 5667 − 3778 = 1889, matching the given condition. For Pavan: expenditure = 3y = 3 * 1889 = 5667, and income = 7556, so savings = 7556 − 5667 = 1889 as well. Both the ratios and equal savings are satisfied.

Why Other Options Are Wrong:
• 6548, 5667 and 8457 do not equal 4 * 1889 and do not satisfy both income and expenditure ratio conditions with equal savings.

Common Pitfalls:
Sometimes candidates incorrectly assume that savings ratios follow the same pattern as income or expenditure ratios, which is not generally true. Another common mistake is to mis-handle the simultaneous equations, for example by subtracting in the wrong direction or arithmetic slip while computing 4 * 1889.

Final Answer:
Therefore, Pavan's monthly income is Rs. 7556.