A clock was set correct at 8 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 1
The correct answer is Option (1) → 35°
A clock that loses 10 minutes per hour moves only 50 minutes for every 60 minutes that really pass. It was set right at 8 o’clock, so one real hour later it shows 8:50, and the angle is read on the clock as it stands.
The hour hand moves 30° an hour, that is, 0.5° a minute. At 8:50 it is \(8\times30+50\times0.5=265^\circ\) past the 12
The minute hand moves 6° a minute. At 50 minutes it is \(50\times6=300^\circ\) past the 12
Angle between the hands \(=300^\circ-265^\circ=35^\circ\)
Tip: At H hours M minutes, the angle between the hands is \(\left|30H-\frac{11}{2}M\right|\). Here \(\left|240-275\right|=35^\circ\). Work out first what time the faulty clock shows, then use the formula.