Question

A clock started at noon. By 10 min past 5, the hour hand has turned through
A.$145^\circ $
B.$150^\circ $
C.$155^\circ $
D.$160^\circ $

Answer 1

Hint: In the above question, a clock has started from 12 noon. After 10 min past 5, the time will be 5:10 PM. If you see a clock at your home, then you must realize that it covers $360^\circ $in 12 hours. Then we can easily know that in 1 hour it will cover $30^\circ $. Now, we can easily find the angle created by an hour hand in 5 hours 10 minutes. Before we find an angle, we need to convert 10 minutes into an hour. Then finally we can find the angle created by hour hand. Let’s see how we can find it.

Complete step-by-step answer:
A clock started at noon. It means it was 12:00 PM.
10 min past 5 means the time on clock will be 5:10 PM
Now, we will convert 5 hours 10 min into an hour.
We know that, 60 min = 1 hours
$ \Rightarrow $10 min = $\dfrac{1}{{60}} \times 10 = \dfrac{1}{6}$hours
 5 hours 10 min = 5 + $\dfrac{1}{6}$= $\dfrac{{31}}{6}$hours
In a clock, angle created by hour hand in 12 hours = $360^\circ $.
In a clock, angle created by an hour hand in 1 hours = $\dfrac{{360}}{{12}}$= $30^\circ $.
In a clock, angle created by hour hand in $\dfrac{{31}}{6}$hours = $30 \times \dfrac{{31}}{6}$= 155$^\circ $(Ans.)
Hence, Option C is the correct option.

Note: Students you can solve this question with different methods. Let’s see how can we solve it:
We know that in 12 hours, a clock creates $360^\circ $.
And we know that, 1 hour = 60 min
Then in 12 hours, we have 720 minutes.
So, we can also write;
720 minutes clock creates angle = $360^\circ $
And we have to find an angle created in 5 hours 10 min.
So, now we will convert them in minutes.
5 hours = 300 min
5 hours 10 min = 300 + 10 = 310 minutes
Angle created by hour hand in 310 minutes = $\dfrac{{360}}{{720}} \times 310 = 155^\circ $(Ans.)