Question

The angle between the minute hand and the hour hand of the clock when the time is 8:25 am is?
a) ${{92}^{0}}45'$
b) ${{102}^{0}}30'$
c) ${{105}^{0}}$
d) ${{107}^{0}}15'$

Answer 1

Hint: We are going to use some formulas to calculate the degree for the hour hand of the clock at 8 and then we will calculate the angle made by the minute hand of the clock in 25min then we will subtract these two and then we will convert degree to minutes to get to the final answer.

Complete step-by-step answer:

We are going to solve this question by stating some useful formula that will be needed,

In clock a full round equals to \[{{360}^{0}}\]

i.e. 60 minutes = \[{{360}^{0}}\]

1 minute= ${{6}^{0}}$

Now we will do the same thing for hour,

12 hours = \[{{360}^{0}}\]

1 hour= ${{30}^{0}}$

Now, 8 hours means $8\times {{30}^{0}}={{240}^{0}}$

Now for another 25 minute it will travel another $\dfrac{30}{60}\times 25=12.5$ ,

Now the total angle made by hour hand will be,

Total angle in degree= 240+12.5 = 252.5

And the minute hand will create $25\times 6={{150}^{0}}$ angle.

Now the angle in between hour hand and minute hand will be 252.5 – 150 = ${{102.5}^{0}}$

 $\begin{align}

  & {{1}^{0}}=60' \\

 & {{0.5}^{0}}=30' \\

\end{align}$

Using this in ${{102.5}^{0}}$ we get ${{102}^{0}}30'$ .

Hence option (b) is correct.

Note: This question is a little bit tricky as one should also consider the change in hour hand when the minute hand covers 25 min. And we have stated all the required formulas that should be kept in mind and one should also know how to convert degrees to minutes.