The correct answer is Option 1, 7.5 degrees east longitude.

To understand why, let`s first consider the concept of time zones. Time zones are defined based on the Earth`s rotation and are divided into 24 equal sections, each representing an hour. As you move from east to west, each time zone is approximately 15 degrees apart.

In India, the standard time zone is GMT +5:30, which means that India is 5 hours and 30 minutes ahead of Greenwich Mean Time (GMT).

Now, if it is 1:00 PM in India, it means that the local time in India is 1:00 PM. To find the time on a different meridian, we need to calculate the time difference, considering the rotation of the Earth.

Given that the time difference between India and the meridian in question is 5 hours and 30 minutes, we need to find the meridian that is exactly 5 hours and 30 minutes behind Indian standard time. Since each hour corresponds to approximately 15 degrees of longitude, 5 hours and 30 minutes correspond to 82.5 degrees of longitude.

Therefore, on the meridian located at 7.5 degrees east longitude, the local time would be