Question

The angle through which the minute hand of the clock moves from 08:00 to 08:35 is
A. ${{210}^{\circ }}$
B. ${{90}^{\circ }}$
C. ${{60}^{\circ }}$
D. ${{45}^{\circ }}$

Answer 1

Hint: We first find the minute difference between 08:00 and 08:35. Then we use the relation that the minute hand takes 60 minutes to complete a whole circle. We use proportionality to find the angle between 08:00 to 08:35.

Complete step by step solution:
The minute hand takes 60 minutes to complete a whole circle. The angle that it covers during that is ${{360}^{\circ }}$.
Now we find the difference of time between 08:00 and 08:35. It is 35 minutes.
We have to find the angle that it covers during this time.
We have been given the relation between two variables where we assume the angle as r and time difference as t.
The inversely proportional number is actually directly proportional to the inverse of the given number. The relation between r and t is inverse relation.
It’s given r varies inversely as t which gives $r\propto t$.
To get rid of the proportionality we use the proportionality constant which gives $r=kt$.
Here, the number k is the proportionality constant. It’s given $r=360$ when $t=60$.
We put the values in the equation $r=kt$ to find the value of k.
So, $360=k\times 60\Rightarrow k=\dfrac{360}{60}=6$.
Therefore, the equation comes with the value of k as $r=6t$.
Now we simplify the equation to get the value of r for minute difference being 35
\[r=6\times 35=210\]
Therefore, the angle difference is ${{210}^{\circ }}$. The correct option is A.

Note: In case of angles, we could have also used the fact that the percentage of the whole circle that the minute hand covered in its journey of 35 minutes. The solution would have been the same in that case also.