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°
To solve this, we first need to determine what time the clock actually shows after two hours of "real" time.
Calculate the time shown on losing clock
-
Start Time: 7:00 PM
-
Real time elapsed: 2 hours
-
Loss rate: 15 minutes per hour
-
Time Lost: 30 minutes (15 min/h × 2h)
In a normal clock, the time would be 9:00 PM. Since this clock lost 30 minutes, the time it shows is: 8:30 PM
Calculate the angle at 8:30
To find the angle between the hands at 8:30, we use the standard clock angle formula:
Angle = |30H - 5.5M|
Where H is hours and M is minutes.
-
H = 8
-
M = 30
Angle = |30(8) - 5.5(30)|
Angle = |240 - 165|
Angle = 75°