Tips on cracking Aptitude Questions on Clocks

1. 3 TIPS on cracking Aptitude Questions on Clocks

2. 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

3. Tip #2: For problems on angles, draw diagrams to simplify the problem 12 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 y x 9 3 6 12 x 9 3 y 8 7 6

4. 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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