The opening time of Central Government Offices in India is 9:00 a.m. IST, what…

India follows a single standardised clock (IST) referenced to one fixed meridian — 82°30′ East (82.5°E), which passes near Mirzapur, Uttar Pradesh — instead of each place keeping its own local solar time. Because Earth rotates 360° in 24 hours, every 1° of longitude corresponds to a time difference of 4 minutes (1440 minutes ÷ 360°). A place lying east of the standard meridian experiences sunrise earlier, so its local time runs ahead of IST by that amount; a place lying west of the standard meridian experiences sunrise later, so its local time runs behind IST by that amount.

1. Find each location's longitude difference from the standard meridian (82°30′E = 82.5°E).

   • Chennai: 82.5° − 80° = 2.5°, and Chennai lies west of the standard meridian.

   • Itanagar: 92°45′E = 92.75°E; 92.75° − 82.5° = 10.25°, and Itanagar lies east of the standard meridian.

2. Convert each longitude difference to a time offset using 4 minutes per degree.

   • Chennai: 2.5° × 4 minutes/degree = 10 minutes.

   • Itanagar: 10.25° × 4 minutes/degree = 41 minutes.

3. Apply the offset in the correct direction relative to IST (9:00 a.m.).

   • Chennai (west of standard meridian, so behind IST): 9:00 a.m. − 10 minutes = 8:50 a.m.

   • Itanagar (east of standard meridian, so ahead of IST): 9:00 a.m. + 41 minutes = 9:41 a.m.

Cross-check: the longitude gap directly between Chennai (80°E) and Itanagar (92°45′E) is 12°45′ = 12.75°, which should correspond to a time gap of 12.75° × 4 = 51 minutes between their local times. Checking: 9:41 a.m. − 8:50 a.m. = 51 minutes — this matches, confirming the two computed local times are mutually consistent.

Result: the Central Government Offices open at 8:50 a.m. local time in Chennai and 9:41 a.m. local time in Itanagar.