The priest tells a devotee, 'The temple bell is rung at regular intervals of 45 minutes. The last bell was rung five minutes ago, and the next bell is due to be rung at 7:45 a.m.' At what time did the priest give this information to the devotee?

Introduction / Context:
This question is another timetable and interval problem, framed around the ringing of a temple bell. You are given the regular interval between rings, the time of the next ring, and how long ago the last bell rang relative to when the priest spoke. The aim is to determine the exact time the priest made his statement by working backwards and forwards with these intervals.

Given Data / Assumptions:
- The bell is rung at regular intervals of 45 minutes. - The priest says the last bell was rung five minutes ago. - He also says the next bell is due at 7:45 a.m. - Bell timings strictly follow the 45 minute schedule.

Concept / Approach:
The ringing times of the bell form a sequence with a difference of 45 minutes. If we know one scheduled time (7:45 a.m. for the next bell), we can find the immediately previous scheduled time by subtracting 45 minutes. This previous scheduled time must be the “last bell” mentioned by the priest. Since that last bell rang five minutes before he spoke, we find the time of the priest's statement by adding 5 minutes to the time of the last ring.

Step-by-Step Solution:
Step 1: Note that the bell rings every 45 minutes. Step 2: The next scheduled bell is at 7:45 a.m. Step 3: The previous bell before 7:45 a.m. must have rung 45 minutes earlier. Step 4: Subtract 45 minutes from 7:45 a.m.: 7:45 a.m. minus 45 minutes equals 7:00 a.m. Step 5: Thus, the last bell was rung at 7:00 a.m. Step 6: According to the priest, the last bell was rung five minutes ago at the time he was speaking. Step 7: Therefore, the priest spoke five minutes after 7:00 a.m. Step 8: Add 5 minutes to 7:00 a.m. to get 7:05 a.m. Step 9: Hence, the priest gave this information at 7:05 a.m.

Verification / Alternative check:
We can verify by reconstructing the sequence of bell times around the statement. If a bell rang at 7:00 a.m., and the priest spoke at 7:05 a.m., then indeed the last bell was five minutes ago. Adding the 45 minute interval to 7:00 a.m. gives 7:45 a.m. as the next ringing time, which matches the priest's information. Since both conditions are satisfied simultaneously, 7:05 a.m. is consistent and correct.

Why Other Options Are Wrong:
7.40 am: If the priest spoke at 7:40 a.m., five minutes earlier would be 7:35 a.m., which is not 45 minutes before 7:45 a.m. 7.00 am: This would mean the last bell and the time of speaking are the same, contradicting the statement that the bell was rung five minutes ago. 6.55 am: Five minutes earlier would be 6:50 a.m., and 45 minutes after 6:50 a.m. is 7:35 a.m., not 7:45 a.m.

Common Pitfalls:
Some students subtract the 5 minute gap from 7:45 a.m. instead of applying it to the previous bell time, mixing up the roles of the interval and the “time since last bell.” Others may subtract 45 minutes from the wrong reference point. Keeping track of which times are scheduled (7:00 a.m. and 7:45 a.m.) and which relate to the priest's speech (five minutes after the last bell) avoids these mistakes.

Final Answer:
The priest gave the information to the devotee at 7:05 a.m.