Clock Formulas

Sample Clock Questions With Solution

Question 1: What is the angle between the hands at 6: 30?

Solution:

Angle = |(30 x Hour – 5.5 x Minutes)|

where Hour is the hour hand position and Minutes is the minute hand position.

At 6:30:
Hour = 6
Minutes = 30

Angle = |(30 x 6 – 5.5 x 30)| = |(180 – 165)| = |15| = 15 degrees

So, the angle between the hour and minute hands at 6:30 is 15 degrees.

Question 2: What is the angle between the hands at 2: 45?

Solution:

Angle = |(30 x Hour – 5.5 x Minutes)|

Where:
Hour = 2 (the given hour)
Minutes = 45 (the given minutes)

Let’s calculate the angle:

Angle = |(30 x 2 – 5.5 x 45)| = |(60 – 247.5)| = |(-187.5)| = 187.5 degrees

So, the angle between the hour and minute hands at 2:45 is 187.5 degrees.

Question 3: If the minute hand of a clock is at 3 and the hour hand is at 2, what is the angle between the hands?

Solution:

To find the angle between the hands, use the formula: Angle = |(30 x Hour – 5.5 x Minutes)|

Angle = |(30 x 2 – 5.5 x 3)| = |(60 – 16.5)| = 43.5 degrees

So, the angle between the hour and minute hands is 43.5 degrees.

Question 4: At what time between 4 o’clock and 5 o’clock will the hour and minute hands be exactly 120 degrees apart?

Solution:

For hour and minute hands 120 degrees apart, we can use the formula:

Angle = |(30 x Hour – 5.5 x Minutes)|

Let’s check all the times between 4 o’clock and 5 o’clock and check the angle:

4:00 = Angle = |(30 x 4 – 5.5 x 0)| = |(120 – 0)| = 120 degrees (Exactly 120 degrees)

Therefore, the hour and minute hands will be exactly 120 degrees apart at 4:00.

Question 5: How many times do the hour and minute hands of a clock overlap in a 24-hour period?

Solution:

The hour hand overlaps the minute hand 11 times in every 12-hour cycle.

In a 24-hour period, there are two 12-hour cycles.

So, the total number of overlaps in 24 hours = 11 + 11 = 22 times.