At what time (approximately) (in PM) for the first time after 2:00 PM minute hand and hour hand of the clock will make an angle of 30 degrees?
Show answer & explanation
Correct answer: B
Explanation
The formula for calculating the angle (θ) between the two hands is:
θ = |30H - 5.5M|
Where:
H = Hour (Here, H = 2)
M = Minutes
Calculation Steps
We need to find the value of M (minutes) for which θ = 30°.
Substituting the values into the formula:
30 = |30(2) - 5.5M|
30 = |60 - 5.5M|
Two cases are possible here:
Case 1 (The minute hand is behind the hour hand):
60 - 5.5M = 30
5.5M = 60 - 30
5.5M = 30
Case 2 (The minute hand has crossed the hour hand):
5.5M-60= 30
5.5M = 90
Selecting the Correct Option
Immediately after 2:00, the 30° angle will be formed for the first time at approximately 2:05 (i.e., 2 hours and 5.45 minutes).
Correct Answer: B) 2:05