The average salary of A, B, and C is Rs. 10,000. Only A's average monthly expenditure is known to be Rs. 6000. What is the average savings of B and C together?
Correct Answer: can't be determined
Introduction / Context:Sometimes average problems do not supply enough information to isolate unknowns for a subgroup. Recognizing insufficiency is as important as computing a value when possible.
Given Data / Assumptions:
- Average salary of A, B, C = Rs. 10,000 ⇒ total salary = Rs. 30,000
- Only A's average expenditure is known: Rs. 6000
- Expenditures or savings of B and C are not provided.
Concept / Approach:To compute the average savings of B and C, we need their incomes (known only in total with A) and their expenditures (unknown). Without at least the combined expenditure of B and C, infinitely many distributions satisfy the constraints, leading to different savings outcomes.
Step-by-Step Solution:
Total salary = Rs. 30,000 (for A, B, C) Let expenditures be: A = 6000, B = x, C = y (unknown) Savings(B + C) = (salary(B) + salary(C)) - (x + y) However, salary(B) + salary(C) is not known individually, and x + y is also unknown.Verification / Alternative check:Different choices of B and C expenditures produce different savings while respecting the given information. Hence no unique value exists.
Why Other Options Are Wrong:
- Rs. 5500, Rs. 4500, Rs. 4000: Each assumes extra information not provided.
- None of these: Insufficiency is explicitly captured by “can't be determined.”
Common Pitfalls:Assuming B and C have the same expenditure as A or that the group average for expenditure is known; neither is given.
Final Answer:can't be determined