Question

How many degrees has the hour hand of a clock moved from its position at noon, when the time is 4.24 pm? Choose the correct answer from the given options
(A) ${134^ \circ }$
(B) ${135^ \circ }$
(C) ${132^ \circ }$
(D) ${130^ \circ }$

Answer 1

Hint:As we know that the hour hand of the clock makes ${360^ \circ }$in 12 hours. So, in 1 hour, the hour hand moves ${30^ \circ }$. Now we divide this by 60 minutes and we get the degrees of hour hand made in 1 minute. Then we calculate the minutes at 4.24 pm. Now we multiply the degrees of hour hand made in 1 minute and minutes at 4.24 pm.

Complete step-by-step answer:
According to the question we have to find the degree of hour hand made at 4.24 pm
As we know that in 12 hours a clock made angle = ${360^ \circ }$
Now the angle made by the hour hand of the clock in 1 hour = $\dfrac{{{{360}^ \circ }}}{{12}}$
        \[ = {30^ \circ }\]
So, the angle made by the hour hand of the clock in 1 minute= $\dfrac{{30}}{{60}}$
         $ = {\dfrac{1}{2}^ \circ } = {0.5^ \circ }$
As we know that 1 hour = 60 minutes
Now we calculate the total number of minutes from 12.00 to 4.24 pm we get
$ = 4 \times 60 + 24$
$ = 240 + 24$
$ = 264$
Therefore the total number of minutes=264 minutes
Now we calculate the angle made by clock in 264 minutes we get
$ = 264 \times \dfrac{1}{2}$
$ = {132^ \circ }$
The angle made by the hour hand of the clock at 4.24 pm is ${132^ \circ }$

So, the correct answer is “Option C”.

Note:For solving these type of questions we have to always remember that the angle made by the hour hand is ${360^ \circ }$. Therefore we divide it by 12 hours, this gives us the angle made by the clock per hour i.e. \[{30^ \circ }\].Lastly calculate the total number minutes made by the hour hand for a given time.