Question

The angle between the hands of a clock when the time IS 4.25 AM is:
(a). $17{{\displaystyle \frac{1}{2}}}^{\circ }$
(b). $14{{\displaystyle \frac{1}{2}}}^{\circ }$
(c). $13{{\displaystyle \frac{1}{2}}}^{\circ }$
(d). $12{{\displaystyle \frac{1}{2}}}^{\circ }$

Answer 1

Hint: At first calculate how much the hour hand moves per hour and per minute.
Then calculate how much the minute hand moves per minute. Then find out the difference between them.

Complete step-by-step answer:
A clock is a circle. A circle always contains 360 degrees. A clock is divided up into 12 sectors, based on the numbers 1 to 12.
The hour hand of a clock moves 360 degrees in 12 hours.
So in one hour it will move ${\displaystyle \frac{360}{12}}=30$ degrees.
Again we can say that the hour hand moves 30 degrees in 1 hour or 60 minutes.
 In 60 minutes it can move 30 degrees.
In one minute it can move ${\displaystyle \frac{30}{60}}={\displaystyle \frac{1}{2}}={0.5}^{\circ }$
Now the minute hand of the clock completes a circle in one hour or we can say 60 minutes.
Therefore, in 60 minutes the minute hand moves 360 degrees.
So in one minute the minute hand can move ${\displaystyle \frac{360}{60}}=6$ degrees.
Now, the given time is 4.25 AM.
In 4 hour the hour hand will move $30\times 4=120$ degrees.
In 25 minutes the hour hand will move $0.5\times 25=12.5$ degrees.
So the hour hand will move $120+12.5=132.5$ degrees in total.
In 25 minute the minute hand will move $25\times 6=150$ degrees.
So the difference between the angle of the minute hand and the hour hand is:
${(150-132.5)}^{\circ }={17.5}^{\circ }$
$17.5=17{\displaystyle \frac{5}{10}}=17{\displaystyle \frac{1}{2}}$
Therefore the angle between the hands of a clock when the time is 4.25 AM is $17{{\displaystyle \frac{1}{2}}}^{\circ }$.
Hence, option (a) is correct.

Note: We generally make mistakes while calculating the movement of the hour hand. Generally we forget to add the minute part. Like here the time is 4.25 AM. That means the hour hand moves for 4 hours and 25 minutes. We have to calculate how much the hour hand moves in 25 minutes separately.