Bus interval reasoning — Buses leave every 30 minutes. An inquiry clerk says, “The last bus left 10 minutes ago and the next bus leaves at 9:35 am.” At what time did the clerk give this information?

Introduction / Context:
This problem combines fixed departure intervals with two reference statements: the last departure was 10 minutes ago, and the next is scheduled at a specific absolute time. These two facts let us pin down the current time without enumerating the entire schedule.

Given Data / Assumptions:

• Buses depart every 30 minutes (e.g., at hh:05 and hh:35, or hh:00 and hh:30 depending on alignment).
• Next bus leaves at 9:35 am.
• Previous bus departed 10 minutes before the present moment.

Concept / Approach:
If the next bus is at 9:35 am and intervals are 30 minutes, the prior scheduled departure was at 9:05 am. If the last bus left 10 minutes ago, and that last bus is the 9:05 departure, then the current time is 10 minutes after 9:05 am.

Step-by-Step Solution:
Next bus: 9:35 ⇒ prior bus: 9:05 (30-minute cadence).“Left 10 minutes ago”: now = 9:05 + 0:10 = 9:15.Therefore, the clerk spoke at 9:15 am.

Verification / Alternative check:
From 9:15 am, next at 9:35 is 20 minutes ahead; previous at 9:05 is 10 minutes earlier—both statements match.

Why Other Options Are Wrong:
9:10 would imply a 9:00 or 8:40 schedule; 8:55 or 9:08 do not align with a 9:35 next departure and a 30-minute interval with the given “10 minutes ago” constraint.

Common Pitfalls:
Mistaking the previous departure for 9:30 or confusing “10 minutes ago” as relative to the next bus instead of the previous one.

Final Answer:
9 : 15 am