Question

In a clock having a circular scale of twelve hours, when time changes from 7:45 A.M. to 7:47 A.M., by how many degrees the angle formed by the hour hand and minute hand changes?

• A. 10
• B. 11
• C. 12
• D. 15
• E. None of these

Hint:

Clock angle problems = relative speed of hands. Minute hand $=6^\circ$ per min, Hour hand $=0.5^\circ$ per min. Subtract to find rate of change.

Answer 1

The Correct Option is B

Step 1: Angular speeds.
- The hour hand completes $360^\circ$ in 12 hours $\Rightarrow$ in 1 hour it covers $30^\circ$.
Thus in 1 minute, hour hand moves: \[ \frac{30}{60}=0.5^\circ \] - The minute hand completes $360^\circ$ in 60 minutes.
So in 1 minute, minute hand moves: \[ \frac{360}{60}=6^\circ \] Step 2: Relative motion per minute.
In each minute, the difference in motion between the two hands = \[ 6 - 0.5 = 5.5^\circ \] Step 3: Change in 2 minutes.
From 7:45 A.M. to 7:47 A.M. = 2 minutes. Hence change = \[ 2 \times 5.5 = 11^\circ \] Final Answer: \[ \boxed{11^\circ} \]