Tips on cracking Aptitude Questions Based on Clocks

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3 TIPS on cracking Aptitude Questions on Clocks
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Tip 1 Understand the basics of clock hand
rotation

• Angle covered by the second hand in 60 seconds
  360
• Angle covered by the second hand in 1 second
  6
• Angle covered by the minute hand in 60 minutes
  360
• Angle covered by the minute hand in 1 minute
  6
• Angle covered by the hour hand in 12 hours
  360
• Angle covered by the hour hand in 1 hour 30
• 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

AM 1200 105 210 315 420 525 630 735 840 945 1050
PM 1200 105 210 315 420 525 630 735 840 945 1050
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Tip 2 For problems on angles, draw diagrams to
simplify the problem
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Question Calculate the reflex angle (greater
angle) between the hands of a clock at
1025. Solution The minute hand moves 6 per
minute gt 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 gt x m x 6 The hour
hand moves 1/2 per minute gt y 30 m x ½ m x
6 30 m x ½ gt m 60/11 minutes 5 5/11
minutes
y
x
3
9
6
12
x
3
9
y
8
7
6
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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 gt t 9 hrs gt 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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