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Simple way to solve clock based problems in Aptitude Section

Clock based problems are one of the frequently asked questions in most of the competitive
exam. To solve these problems, it is always better to understand some of the basic principles and the types of problems that get asked. In this post I hereby explained simple tricks and some simple formulas for solving clock based problems.

In every competitive exams clock questions are categorized in to two ways.
  • Problems in angles
  • Problems on incorrect clocks
Problems in angles  

Method :1

Before we actually start solving problems on angles, we need to know couple of basic facts clear:
  • Speed of the hour hand     = 0.5 degrees per minute (dpm)
  • Speed of the minute hand  = 6 dpm
  • At ‘n’ o’ clock, the angle of the hour hand from the vertical is 30n
The questions based upon these could be of the following types

Example : 1  
   What is the angle between the hands of the clock at 7:20
At 7 o’ clock, the hour hand is at 210 degrees from the vertical.
In 20 minutes,
Hour hand = 210 + 20*(0.5) = 210 + 10 = 220 {The hour hand moves at 0.5 dpm}
Minute hand = 20*(6) = 120 {The minute hand moves at 6 dpm}
Difference or angle between the hands = 220 – 120 = 100 degrees

Method : 2

Example :2  
     Find the reflex angle between the hands of a clock at 05.30?
The above problem are solved by the bellow formula
Angle between X and Y =|(X*30)-((Y*11)/2)|
Angle between hands at 5:30
Step 1:  X=5 , Y=30
Step 2:  5*30=150
Step 3:  (30*11)/2 = 165
Step 4:  165-150=15
Thus, angle between hands at 5:30 is 15 degrees.

Method : 3

Example : 3 
   At what time 3&4’o clock in the hands of clock together.
Approximately we know at 03:15 hands of the clock together
So 15*60/55=16.36 min

Problems on incorrect clocks

Such sort of problems arise when a clock runs faster or slower than expected pace. When solving these problems it is best to keep track of the correct clock.

Example : 4 
    A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day?
The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour.
From 8 AM to 10 PM on the same day, time passed is 14 hours.
In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.
So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

Important Notes
  • Two right angles per hour(Right angle = 90, Straight angle=180)
  • Forty four right angles per day
  • Between every two hours the hands of the clock coincide with each other for one time except between 11, 12 and 12, 1.In a day they coincide for 22 times.
  • Between every two hours they are perpendicular to each other two times except between 2, 3 and 3, 4 and 8, 9 and 9, 10.In a day they will be perpendicular for 44 times.
  • Between every two hours they will be opposite to each other one time except between 5, 6 and 6, 7.In a day they will be opposite for 22 times.
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