Tip #2: For problems on angles, draw diagrams to simplify the problem

Question: Calculate the reflex angle (greater angle) between the hands of a clock at 10:25.

Solution:

The minute hand moves 6° per minute => x = 25 x 6 = 150°

The hour hand moves 1/2° per minute.

At 1 hr 35 minutes to noon, y = 95 x ½ = 47.5°

Angle between the hands = x + y = 197.5°

Question: At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?

Solution:

Let us assume that at m minutes past 7, the hands are at 180°

At m minutes past 7, x = y

The minute hand moves 6° per minute => x = m x 6

The hour hand moves 1/2° per minute => y = 30 + m x ½

m x 6 = 30 + m x ½

=> m = 60/11 minutes = 5 5/11 minutes

Tip #3: For problems on incorrect clocks, keep track of the correct time

Question: A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:

Solution:

The incorrect watch gains 5 seconds in 3 minutes, i.e., 100 seconds in 1 hour.

If 3600 seconds have elapsed, the incorrect watch will advance by 3700 seconds.

If 1 hr has elapsed, the incorrect watch will advance by 37/36 hrs.

Let the actual time elapsed be ‘t’ hrs. In time t, the watch will advance by 37/36 x t hrs.

From 7 a.m. till quarter past 4, the incorrect watch has advanced by 9.25 hrs = 37/4 hrs.

37/36 x t = 37/4 => t = 9 hrs => True time = 4 PM

Question: A watch gains 5 sec in 3 min and was set right at 8 AM. What time will it show at 10 PM on the same day?

Solution:

The incorrect watch gains 5 seconds in 3 minutes, i.e., 100 seconds in 1 hour.

From 8 AM to 10 PM on the same day, time passed = 14 hours.

=> In 14 hours, the incorrect watch would gain 1400 seconds = 23 minutes 20 seconds.

=> When the correct time is 10 PM, the incorrect watch would show 10: 23: 20 PM.

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Clocks

Clock Problems: Alarm clock angle Math Problems, Clock Angle problems with solutions, Clock Problems Shortcut formulas