Question

What is angle between the two hands ofclock when it is 10 : 25 in the?

Answer 1

Based on the numbers 1 to 12 in a clock, a clock is divided into 12 sectors, each of 360° / 12 = 30° each. The angular distance between two consecutive time indicators (numbers in the clock) is 30°.

Here, at 10:25, the hour hand is at 10 and the minute hand is at 5.

Thus there will be a difference of 10 - 5 = 5 sectors of 30° each between the two hands, thus the minute difference between them will be 5 × 30 = 150°.

But, as the angular distance between two consecutive time indicators is 30°, the hour hand travels an angular distance of 30° in an hour, i.e., 60 minutes.

Thus,

→  Angular distance travelled by the hour hand in 60 minutes = 30°

→  Angular distance travelled by the hour hand in 1 minute = (1/2)°

According to this, from 10:00 to 10:25, as there's a difference of 25 minute,

→  Angular distance travelled by the hour hand in 25 minutes = (25/2)° = 12.5°.

So the hour hand travels 12.5° during this time in clockwise direction, thus the angle between the two hands will be more than 150°.

Hence the actual angle is 150° + 12.5° = 162.5°