A clock was set correct at 10 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?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 25°
The angle is measured on what the clock shows, not on the correct time. The clock was right at 10 o’clock and loses 10 minutes in every hour.
After one hour, the clock has moved only \(60-10=50\) minutes, so it shows 10:50.
The minute hand moves 6° a minute, so at 50 minutes it is at \(50\times6=300^\circ\) from 12.
The hour hand moves 30° an hour and 0.5° a minute, so at 10:50 it is at \(10\times30+50\times0.5=325^\circ\) from 12.
The angle between the hands is \(325^\circ-300^\circ=25^\circ\).
Tip: The angle between the hands at H hours M minutes is \(\left|30H-5.5M\right|\); here \(\left|300-275\right|=25^\circ\).