Question

At what time between 5 and 6 o'clock will the minute and the hour hand be perpendicular to each
other?
​

Answer 1

Answer:

Since you are asking for an angle of 90° between 5 and 6. Thus, at approximately 5 hrs 10.909 mins the needles will be 90° apart.

Answer 2

Answer:

In a minute, the hour hand moves by half degrees and the minute hand moves by six degrees.

The angle at 4 o'clock between the two hands is 120 degrees.

For them to be perpendicular, it should move m minutes

120=90+(6m−

2

m

)

30=

2

12m−m

60=12mm

11m=60

m=5

11

5

It should be 5

11

5

for the two hands to be perpendicular.