Scheduled meeting time from relative earliness/lateness — Anuj arrived on Tuesday at 8:15 h (15 minutes before 8:30 h) and found himself 30 minutes earlier than a man who was 40 minutes late. What was the scheduled meeting time?

Introduction / Context:
Time-of-appointment questions often tie together one person’s early arrival with another’s lateness. The trick is to express both observations relative to the same unknown “scheduled time,” then reconcile the two facts consistently.

Given Data / Assumptions:

• Anuj reached at 8:15 h (since he was 15 minutes before 8:30 h).
• At 8:15 h, Anuj was 30 minutes earlier than a man who was 40 minutes late.
• “Late” and “early” are measured relative to the unknown scheduled time T.

Concept / Approach:
If the other man arrived at time A and was 40 minutes late, then T = A − 40 minutes. Anuj at 8:15 h was 30 minutes earlier than that man, so A = 8:15 h + 30 minutes = 8:45 h. Substitute to obtain T.

Step-by-Step Solution:
Other man’s arrival A = 8:15 + 0:30 = 8:45.He was 40 minutes late ⇒ scheduled T = 8:45 − 0:40 = 8:05.Therefore, the planned meeting time was 8:05 h.

Verification / Alternative check:
At T = 8:05, the late man at 8:45 is +40 minutes; Anuj at 8:15 is −10 minutes. Relative to the late man, Anuj is earlier by 30 minutes (8:45 − 8:15), matching the statement.

Why Other Options Are Wrong:
8:00 and 8:15 fail the 40-minute lateness for the other person given the 8:15/8:45 pair; 8:45 is an arrival, not the scheduled time.

Common Pitfalls:
Confusing “earlier than the late man” with “early relative to the schedule,” or subtracting 40 from 8:15 instead of from the late man’s 8:45 arrival.

Final Answer:
8:05 h