Person A earns 50% of the salary of person B, and person B earns 80% of the salary of person C. If together A, B and C earn a total of Rs. 22,000 in a month, what is the monthly earning of A?

Introduction / Context:
This question connects the monthly salaries of three people through percentage relations. It tests your ability to write one unknown in terms of another and then use the given total to find individual earnings.

Given Data / Assumptions:

• Let C salary per month be C.• B earns 80% of C salary.• A earns 50% of B salary.• Combined monthly earnings of A, B and C are Rs. 22,000.• We must find the monthly salary of A.

Concept / Approach:
First express B in terms of C using the 80% relation. Then express A in terms of C by applying the 50% relation. Add all three salaries to match the total given, and then solve for C. Finally, compute A salary using the relation already derived.

Step-by-Step Solution:
Step 1: B earns 80% of C, so B = 0.80C.Step 2: A earns 50% of B, so A = 0.50B = 0.50 * 0.80C = 0.40C.Step 3: Total earnings = A + B + C.Step 4: Substitute the expressions: total = 0.40C + 0.80C + C.Step 5: Combine like terms: 0.40C + 0.80C + 1.00C = 2.20C.Step 6: Given total = Rs. 22,000, we have 2.20C = 22000.Step 7: So C = 22000 / 2.20 = 10000.Step 8: A salary = 0.40C = 0.40 * 10000 = Rs. 4,000.

Verification / Alternative check:
Check individual salaries. C = 10000, B is 80% of 10000 which is 8000, and A is 50% of 8000 which is 4000. Sum = 10000 + 8000 + 4000 = 22000, matching the given total.

Why Other Options Are Wrong:
Values 4200, 4400 and 4600 do not produce a total of 22000 when used for A in the derived relations. They represent miscalculations of one or more percentages.

Common Pitfalls:
Students may incorrectly add percentages or apply them to the wrong salary. Another frequent error is to treat 50% and 80% as reductions from the same base instead of sequential relations.

Final Answer:
The monthly earning of A is Rs. 4,000.