Efficiency vs. Time — Inverse Relationship A is thrice as efficient as B, and C is twice as efficient as B. What is the ratio of the number of days taken by A, B, and C respectively when working alone?

Introduction / Context:
Efficiency (rate) and time are inversely proportional: higher efficiency means less time for the same work. Converting relative efficiencies to time ratios is a common aptitude step.

Given Data / Assumptions:

• B's efficiency = x.
• A's efficiency = 3x.
• C's efficiency = 2x.

Concept / Approach:
Time ∝ 1/efficiency. Therefore, days_A : days_B : days_C = 1/(3x) : 1/x : 1/(2x) = 1/3 : 1 : 1/2. Multiply by 6 to clear fractions.

Step-by-Step Solution:
Days ratio = 1/3 : 1 : 1/2Multiply by 6 ⇒ 2 : 6 : 3

Verification / Alternative check:
Check inverses against efficiencies: A (3x) gets smallest time; B (x) largest; C (2x) middle — the 2 : 6 : 3 order matches.

Why Other Options Are Wrong:
Any ordering not reflecting the inverse relationship (A shortest, B longest) is incorrect.

Common Pitfalls:
Confusing the direct vs. inverse relation between time and efficiency.

Final Answer:
2 : 6 : 3