If the current time in the USA is 4:15 a.m. and Indian Standard Time (IST) is always 9 hours 30 minutes ahead of USA time, what will be the time in India exactly 18 hours from now?

Introduction / Context:
This is a time zone problem that combines a fixed time difference between two locations with an additional time interval into the future. You are told the present time in the USA, the offset between USA time and Indian Standard Time, and asked to find what the time in India will be 18 hours from now. Such questions test your ability to handle time zone conversions and to track day changes correctly.

Given Data / Assumptions:

• Current time in the USA is 4:15 a.m.
• IST is ahead of USA time by 9 hours 30 minutes (IST = USA time + 9 hours 30 minutes).
• We must find the time in India exactly 18 hours from the current moment.
• We assume the date itself is not required, only the time and whether it is the same day or the next day.

Concept / Approach:
First, determine the current time in India using the given offset between USA time and IST. Once the current IST is known, we add 18 hours to it to find the future IST. Because adding 18 hours can extend into the next calendar day, we must handle the wrap around of the 24 hour clock and state clearly whether the result is on the same day or the next morning.

Step-by-Step Solution:
Step 1: Start with the current USA time: 4:15 a.m. Step 2: Add the time zone difference of 9 hours 30 minutes to convert to IST: 4:15 a.m. + 9 hours 30 minutes = 13:45, which is 1:45 p.m. in India. Step 3: Thus, the current time in India is 1:45 in the afternoon. Step 4: Now we must find the time in India 18 hours from this instant. Step 5: Add 18 hours to 1:45 p.m. First, 12 hours after 1:45 p.m. is 1:45 a.m. the next day. Step 6: There are still 6 more hours to add (since 18 = 12 + 6). Add 6 hours to 1:45 a.m. This gives 7:45 a.m. on the next day in India. Step 7: Therefore, the required time in India is 7:45 in the next morning.

Verification / Alternative check:
In 24 hour format, 1:45 p.m. is 13:45. Add 18 hours to 13:45: 13:45 + 18:00 = 31:45. Since 24:00 corresponds to midnight, subtract 24 hours: 31:45 - 24:00 = 7:45. Because we crossed midnight, the time belongs to the next day. This matches the earlier step by step reasoning and confirms that the time is 7:45 a.m. the next morning.

Why Other Options Are Wrong:
1:45 in the afternoon: This is the current IST, not the time 18 hours later.

7:45 in the evening: That would be only 6 hours after 1:45 p.m., not 18 hours.

1:45 in the next morning: This corresponds to 12 hours after the starting IST, not 18 hours.

10:45 in the evening: This time does not match any natural decomposition of the 18 hour addition from 1:45 p.m.

Common Pitfalls:
A common mistake is to add 18 hours directly to the original USA time without first converting to IST, which mixes time zones incorrectly. Others miscount the day change when the sum exceeds 24 hours and may forget to mark that the result occurs the next day. Using 24 hour format often makes the addition clearer and helps avoid these off by one day errors.

Final Answer:
Eighteen hours from now, the time in India will be 7:45 in the next morning.