Question

Local mean time of a place of longitude of 42°36 W is 8h 42m 15s AM. The corresponding Greenwich Mean Time is
1. 10h 32m 40s AM
2. 11h 32m 39s PM
3. 0 h 32m 39s PM
4. 11 h32m 39s AM

Answer 1

Correct Answer - Option 4 : 11 h32m 39s AM

Concept:

There are 24 hours per day, so in one hour the earth rotates 1/24th of the way around 360 degrees divided by 24 gives an angle measure of 15 degrees per hour of time or 4 degree in one minute.

Longitude line measurements start with the north-to-south line that goes through Greenwich which is 0 degree longitude or prime meridian, and measure in positive numbers to 180 degrees eastward and measures from Greenwich in the negative direction to 180 degrees to westward.  

Local time = GMT ± Longitude

(Take minus sign if longitude is westward and take positive sign if it is eastward)

Calculation:

Local mean time = 8h 42m 15s.

1 minute = 4^° 

Longitude of 42°36 W which is equivalent to 42 × 4 + 36× 4/60 = 170.4 minutes or 2 h 50 m 24 s

Now

8h 42m 15s = GMT - 2 h 50 m 24 s

∴ GMT = 10 h 92m 39 s or 11 h 32 m 39 s AM