A broken clock is set corectly at 12:00 noon. However, it registers only 20 minutes for each hour. In how many hours will it again register the correct time ?
A)12
B)18 analog clock(12h)
C)24
D)30
E)36 digital clock (12h)
1. Analog Clock:
angular velocity real time: ω1=2π12 hangular velocity display time: ω2=2π36 hw2⋅t−w1⋅t=n⋅2π2π12 h⋅t−2π36 h⋅t=n⋅2π|:2π112 h⋅t−136 h⋅t=nt⋅(112 h−136 h)=nt⋅(36−1212⋅36)=nt⋅(2412⋅36)=nt⋅(236)=nt⋅(118)=nt=18⋅n
next correct time, if n = 1, then t = 18 hours.
2. Digital Clock(24h):
angular velocity real time: ω1=2π24 hangular velocity display time: ω2=2π72 hw2⋅t−w1⋅t=n⋅2π2π24h⋅t−2π72 h⋅t=n⋅2π|:2π124 h⋅t−172 h⋅t=nt⋅(124 h−172 h)=nt⋅(72−2424⋅72)=nt⋅(4824⋅72)=nt⋅(272)=nt⋅(136)=nt=36⋅n
next correct time, if n = 1, then t = 36 hours.
