Time conversion with Indian Standard Time (IST): If the standard meridian is 82°30′ E and the IST at longitude 90° E is 8 h 30 m, what is the Local Mean Time (LMT) at 90° E?

Introduction / Context:
Converting between a country’s standard time and local mean time requires accounting for the longitude difference from the standard meridian. Every degree of longitude corresponds to 4 minutes of time.

Given Data / Assumptions:

• Standard meridian for IST = 82°30′ E.
• Station longitude = 90° E.
• IST at the station is 8 h 30 m.

Concept / Approach:
Time difference per degree of longitude = 4 minutes. If a place is east of the standard meridian, its LMT is ahead of standard time by 4 minutes per degree of longitude difference. Longitude difference Δλ = 90°00′ − 82°30′ = 7°30′ = 7.5°. Time lead = 7.5 × 4 = 30 minutes.

Step-by-Step Solution:
Compute Δλ: 90° E − 82°30′ E = 7°30′.Convert to time: 7.5° × 4 min/° = 30 min.Add to IST (since station is east): LMT = 8:30 + 0:30 = 9:00.

Verification / Alternative check:
Reverse check: moving west would subtract time; here we moved east, so LMT must be later than IST—9:00 fits.

Why Other Options Are Wrong:
Times earlier than 8:30 contradict the “east is later” rule; 8:30 ignores the longitude difference.

Common Pitfalls:
Using 1 hour per 15° but forgetting to convert 30′; mixing “ahead” and “behind” directions.

Final Answer:
9 h 00 m.