# Clocks

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

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

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1 Tips

## Learning Pundits Content Team

__3 TIPS on cracking Aptitude Questions on Clocks__

__3 TIPS on cracking Aptitude Questions on Clocks__Looking for Questions instead of tips?- You can directly jump to Aptitude Test Questions on Clocks

__Tip #1__: Understand the basics of clock hand rotation

a) Angle covered by the second hand in 60 seconds = 360°

b) Angle covered by the second hand in 1 second = 6°

c) Angle covered by the minute hand in 60 minutes = 360°

d) Angle covered by the minute hand in 1 minute = 6°

e) Angle covered by the hour hand in 12 hours = 360°

f) Angle covered by the hour hand in 1 hour = 30°

g) Angle covered by the hour hand in 1 minute = 30°/60 = 1/2°

The minute and hour hands coincide 22 times in a day or 11 times in 12 hours. The timing of these coincidences are (approximately):

*NOTE: Between **11 **and 1, they **coincide** only once, i.e., at **12** o'clock*

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__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

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