A temple bell rings every 45 minutes at regular intervals. The last bell rang 5 minutes ago, and the next bell is due at 7:45 a.m. At what time did the priest give this information to the devotee?

Introduction / Context:
Periodic-event problems hinge on the fixed interval and the relationship between the last occurrence, the next occurrence, and the current time. Here, the bell period is 45 minutes.

Given Data / Assumptions:

• Interval = 45 minutes.
• Last bell = 5 minutes ago from the time of speaking.
• Next bell time = 7:45 a.m.

Concept / Approach:
If the next ring is at 7:45 a.m., the previous one must have been at 7:00 a.m. (exactly 45 minutes earlier). Since the last ring was 5 minutes before the speech, the speech was delivered 5 minutes after 7:00 a.m.

Step-by-Step Solution:

Verification / Alternative check:
Forward check: after 7:05 a.m., the next ring is indeed at 7:45 a.m. in 40 minutes (because interval is 45; 5 minutes have passed since 7:00).

Why Other Options Are Wrong:
7:00 a.m. contradicts “last bell 5 minutes ago”; 7:40 a.m. would place the “last bell” at 6:55 a.m., which is not 45 minutes before 7:40 a.m. relative to the 7:45 schedule.

Common Pitfalls:
Adding instead of subtracting with the 45-minute interval, or mixing up which time is “next” vs “previous.”

Final Answer:
7 : 05 am.