Clarifying “times more efficient” and days ratio: Assume X works at a rate five times that of Y (interpreting “4 times more efficient” as X is 5 times as efficient as Y). What is the ratio of the number of days taken by X and Y, respectively, to do the same work alone?

Introduction / Context:
The phrase “4 times more efficient” is ambiguous. In many aptitude settings it is intended to mean “4 times as efficient” (i.e., 4X). However, strictly parsed English can interpret “4 times more than Y” as X = Y + 4Y = 5Y. Under the Recovery-First policy, we make the minimal clarification that renders one of the provided options correct by interpreting X = 5Y so the question is solvable with the given choices.

Given Data / Assumptions:

• Take rate_X = 5 * rate_Y (clarified interpretation).
• Each works alone on the same job.

Concept / Approach:
Time is inversely proportional to rate. Therefore, the ratio of days (X : Y) equals the inverse of the rate ratio (Y : X).

Step-by-Step Solution:
rate_X : rate_Y = 5 : 1days_X : days_Y = 1/5 : 1 = 1 : 5

Verification / Alternative check:
Pick a total work of 1 job. If rate_Y = 1 unit/day ⇒ time_Y = 1 day to do 1 unit (toy illustration). If rate_X = 5 units/day ⇒ time_X = 1/5 day. The ratio of times is 1/5 : 1 = 1 : 5.

Why Other Options Are Wrong:

• 5 : 1 and 8 : 1 are rate-style answers, not time ratios.
• 6 : 8 is unrelated to the 5:1 assumption.

Common Pitfalls:

• Mistaking “times more efficient” for a clean multiplicative factor without clarifying whether it is +4Y or ×4.

Final Answer:
1 : 5