A scooter needs servicing for 2/3 hour every 45 days before overhauling, and 2/3 hour every 60 days after overhauling. What fraction of the pre-overhauling service time is saved after overhauling?

Introduction / Context:
The problem compares periodic service times over different intervals, asking for the fractional saving relative to the original (pre-overhaul) requirement. It tests rate reasoning and fraction comparison over time.

Given Data / Assumptions:

• Pre-overhaul need: 2/3 hour every 45 days.
• Post-overhaul need: 2/3 hour every 60 days.
• We seek the fraction saved relative to the pre-overhaul requirement.

Concept / Approach:
Convert both to a common basis (e.g., hours per day). Then compute (pre - post) / pre. This yields the fraction of time saved compared to the original requirement.

Step-by-Step Solution:

Verification / Alternative check:
Scale to 540 days: Pre total = (2/3) * (540/45) = (2/3) * 12 = 8 hours; Post total = (2/3) * (540/60) = (2/3) * 9 = 6 hours. Saving = 2/8 = 1/4 of pre. Confirms the result.

Why Other Options Are Wrong:

• 4/3, 1/3, 3/4, 1/6: These do not match the computed ratio of time saved to the original time.

Common Pitfalls:

• Comparing absolute hours without normalizing by time window.
• Subtracting 45 from 60 or mixing up reciprocals.

Final Answer:
1/4