The correct answer is A. 7 h 00 m.
The standard time at longitude 90° E is 8 h 30 m. This means that the Sun is at its highest point in the sky at 8 h 30 m at longitude 90° E. At longitude 82° 30′ E, the Sun is at its highest point in the sky 15 minutes earlier, at 8 h 15 m. This is because the Earth rotates on its axis once every 24 hours, and there are 360 degrees in a circle. Therefore, the Earth rotates 15 degrees every hour. Longitude 90° E is 7 1/2 degrees east of longitude 82° 30′ E. Therefore, the Sun is 7 1/2 hours ahead of longitude 82° 30′ E.
The local mean time at a place is the time that would be shown by a sundial at that place. A sundial shows the time by the position of the Sun in the sky. The Sun moves across the sky from east to west, so the time on a sundial increases from east to west. Therefore, the local mean time at longitude 82° 30′ E is 7 h 00 m.