Clocks Solutions – Concept, Shortcut with Examples for Banking IBPS/SBI
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A clock has mainly two hands on the basis of which questions are mainly asked; the smaller one is called the hour handor short hand while the larger one is called the minute hand or long hand.
Important facts related to clocks:
1) In every 60 minutes, the minute hand gains 55 minutes on the hour hand.
2)In every hour, both the hands coincide once.
3) The hands are in the same straight line when they are coincident or opposite to each other. i.e. the angle formed between them is either 0 degrees or 180 degrees.
4) When the two hands are at right angles i.e. 90 degrees, then they are 15 minuteapart.
5)When the hands are in the opposite directionsi.e. 180 degrees,then they are 30 minute apart.
6)Angle traced by hour hand in 12hrs = 360 degrees.
7)Angle traced by minute hand in 60 min = 360 degrees.
8)The hands of a clock coincide in a day or 24 hours is 22 times, in 12hours 11minutes.
9) The hands of clock are straight in a day is 44 times.
10) The hands of a clock are at right angle in a day is 44 times.
11)The hands of a clock in straight line but opposite in direction is22 times per day.
Let us understand the concept of clocks with the help of some examples:
Eg: By how may degrees will the hour hand rotate in 6 hours?
Sol: Angle traced by the hour hand in 6 hours = (360 / 12) * 6
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Eg: How many times the hands of a clock form right angle in a day?
Sol: In 12 hours, they form right angles 22 times.
So, In 24 hours, they form right angles 44 times.
Eg: At what angle the hands of a clock are inclined at 15 minutes past 5?
Sol: Angle traced by hour hand in 21 / 4 hrs = (360 / 12) * (21 / 4) = 157 (1/2)º
Angle traced by min. hand in 15 min. =(360 / 60) * (15)º = 90º
Required angle = 157 (1/2)º – 90º = 67 (1/2) º
Eg: At what time between 4 and 5 o’clock will the hands of a watch point in opposite directions?
Sol: At 4 o’clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
Minute hand will have to gain 50 min. spaces.
As 55 min. spaces are gained in 60 min.
So, 50 min. spaces are gained in (60 / 55) * 50 min.
or 54 (6 / 11) min.
So, Required time = 54 (6 / 11) min past 4.
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