Tips And Tricks And Shortcuts For Clocks

Type 1:  Shortcuts on Clocks.

Question 1. What is the angle between the minute hand and the hour hand when the time is 5:30.

Options:

A.15 °

B. 10°

C. 20°

D. None of the above

Solution:    

Angle covered by the hour hand (H) at 5:30:
Since the hour hand moves 30 degrees for each hour on the clock, at 5:30, it covers 5.5 hours (5 hours and 30 minutes). So, the angle covered by the hour hand is H = 5.5 x 30 = 165°

Angle covered by the minute hand (M) at 5:30:
The minute hand moves 6 degrees for each minute on the clock. At 5:30, it covers 30 minutes. So, the angle covered by the minute hand is M = 30 x 6 = 180°

  Calculating the absolute difference between the two angles,

  Angle between the hour and minute hands (A) = H – M = 165 – 180= 15°

Correct Option: A

Question 2. At what time between 4 o’clock and 5 o’clock will the minute hand and the hour hand of the clock form a 90 ° angle?

Solution:

Let’s assume the time is x minutes past 4 o’clock.

Angle covered by the hour hand in x minutes = \frac{30}{60}\times x = \frac{x}{2}°.

Angle covered by the minute hand in x minutes
=\frac{360}{60}\times x=6x°.

For 90° angle between the hands, the difference between their angles should be 90°.

So, 6x – x/2 = 90

12x – x = 180

11x = 180

x = 180/11 ≈ 16.36 minutes

Therefore, the hands form a 90° angle approximately 16.36 minutes past 4 o’clock.