If the earth’s direction of rotation is reversed, what would be the IST when it is noon at the International Date Line ?

When rotation is reversed, time-zone offsets relative to GMT change sign: the International Date Line becomes GMT+12 (i.e., 12 hours ahead of GMT) and Indian Standard Time becomes GMT−5:30 (5.5 hours behind GMT) [1]. If it is noon (12:00) at the IDL (GMT+12), GMT = 12:00 − 12:00 = 00:00. IST = GMT − 5:30 = 00:00 − 5:30 = 18:30 (6:30 PM) the previous day. The IST definition as time at 82.5°E (normally GMT+5:30) explains the magnitude of the 5.5-hour offset that flips when rotation reverses [2]. Hence the correct answer is 18.30 hrs.

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 18: Latitudes and Longitudes > Explanation: > p. 247
2. [2] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 18: Latitudes and Longitudes > Indian Standard Time > p. 245