Pairwise averages of three people: If avg(Rakesh, Mohan) = 15, avg(Mohan, Ramesh) = 12, and avg(Rakesh, Ramesh) = 13, find Mohan’s age.
Aptitude
Average
Difficulty: Easy
Choose an option
Answer
Correct Answer: 14
Explanation
Introduction / Context:We are given three pairwise averages among Rakesh (Rk), Mohan (Mo), and Ramesh (Ra). Converting to pairwise sums allows elimination and solution for an individual age directly.
Given Data / Assumptions:
- Rk + Mo = 30
- Mo + Ra = 24
- Rk + Ra = 26
Concept / Approach:Add the first two equations to obtain Rk + 2Mo + Ra. Then substitute Rk + Ra from the third equation to isolate Mo.
Step-by-Step Solution:
(Rk + Mo) + (Mo + Ra) = 30 + 24 = 54Rk + 2Mo + Ra = 54But Rk + Ra = 26 ⇒ 26 + 2Mo = 542Mo = 28 ⇒ Mo = 14Verification / Alternative check:Compute individuals: From Rk + Mo = 30, Rk = 16; from Mo + Ra = 24, Ra = 10. Check Rk + Ra = 26, consistent.
Why Other Options Are Wrong:
- 16, 13, 12, 15: do not satisfy all three pairwise sums simultaneously.
Common Pitfalls:Attempting to solve using three variables directly without first converting to pairwise sums and applying elimination succinctly.
Final Answer:14