Question

A clock was set correct at 12 O'clock. It loses 10 minutes per hour. What will be the angle between the hour and minute hands of the clock after one hour?

• A. 90°
• B. 85°
• C. 75°
• D. 105°

Hint:

For clock problems, always account for both hour-hand and minute-hand movement; the smaller angle is usually the answer.

Answer 1

The Correct Option is B

Step 1: Understand the problem. The clock loses 10 minutes every hour. This means that when real time passes 60 minutes, the clock shows only 50 minutes.
Step 2: What happens after one real hour? After 60 minutes of real time, the clock will show 12:50.
At 12:50, the minute hand is at the 50-minute mark.
Step 3: Position of the minute hand. Each minute = \(6^\circ\). So minute hand position = \( 50 \times 6 = 300^\circ \) from 12 o’clock.
Step 4: Position of the hour hand. Each hour mark = \(30^\circ\), and each minute = \(0.5^\circ\) movement for the hour hand.
At 12:50, the hour hand has moved \( 50 \times 0.5 = 25^\circ \) from 12 o’clock.
Step 5: Angle between them. Difference = \( 300^\circ - 25^\circ = 275^\circ \).
We take the smaller angle on the clock, so angle = \( 360^\circ - 275^\circ = 85^\circ \).
Hence, the answer is \(\boxed{85^\circ}\).