A clock was set correct at 7 PM. It loses 15 min/h. What will be the angle between the hour and minute hands of the clock after two hours?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 75°
The question asks for the angle between the hands of this clock, so first find the time it shows. A clock that loses 15 min/h runs slow: for every 60 real minutes, its hands move only 45 minutes (60 − 15).
The time the clock shows:
In 2 real hours it moves \(2\times45=90\) minutes, that is, 1 h 30 min
It was set right at 7:00, so it shows 7:00 + 1 h 30 min = 8:30
The angle at 8:30 (the minute hand moves 6° a minute, the hour hand 30° an hour):
Minute hand at 30 minutes: \(30\times6^{\circ}=180^{\circ}\) from the 12
Hour hand halfway between 8 and 9: \(8.5\times30^{\circ}=255^{\circ}\) from the 12
Angle between the hands \(=255^{\circ}-180^{\circ}=75^{\circ}\)
