Clocks Aptitude Important Formulas, tricks and shortcut Methods:
(I) Minute Spaces: The face or dial of watch is a circle whose circumference is divided into 60 equal parts, called minute spaces.
(II) Hour Hand and Minute Hand: A clock has two hands. The smaller one is called hour hand or short hand while the larger one is called minute hand or long hand.
(III) The minute space traces an angle of 360°. Therefore, 1 minute space traverses an angle of 6°.
In 1 hour, minute hand traverses 60 minute space or 360°, hour hand traverses 5 minute space or 30°
(IV) Important key Points:
- In every hour, both the hands coincide once.
- The hands are in the same straight line when they are coinciding or opposite to each other.
- When the two hands are right angles, they are 15 minute spaces apart.
- When the hands are in opposite directions, they are 30 minutes space apart.
- Angle traced by hour hand in 12 hours = 360°
- Angle traced by hour hand in 60 minutes = 360°
- If a watch or clock indicates 8:15 when correct time is 8, it is said to be 15 minutes too fast.
- If a watch or clock indicates 7:45 when correct time is 8, it is said to be 15 minutes too slow.
- The hands of the clock are perpendicular to each other for 22 times in 12 hours and 44 times in a day.
- The hands of the clock are opposite to each other for 11 times in 12 hours and 22 times in a day.
- The hands of the clock are coincide to each other for 11 times in 12 hours and 22 times in a day.
- The hands of clock are 44 times in a straight line per day.
- The minute hand gain 55 minutes over hour hand per hour.
At what time between 2’O clock and 3’O clock, the hands of the clock are opposite to each other?
Solution:At 2’O clock, the minute hand will be at 12 as shown bellow.
I.e. totally it should gain (10 + 30) = 40 minutes spaces to be opposite to that of hour hand.
We know that,
Minute hand gains 55 minutes spaces over hour hand in 1 hour.
Therefore, minute hand gain 40 minute spaces over hour hand in 40 × (60/55) = 43(7/11)
Hence, the hand of the clock will be opposite to each other at 43(7/11) minutes past 2’O clock.
My watch, which gains uniformly, is 2 minutes and show at noon on Sunday, and is 4 minute 48 seconds fast at 2 p.m on the following Sunday. When it was correct?
From Sunday noon to the following Sunday at 2 p.m there are 7 days 2 hours or 170 hours.
The watch gains 2 + 4(4/5) minutes in 170 hrs
Therefore, the watch gains 2 min in 2/[6(4/5)] × 170 hours. I.e. 50 hours.
Now, 50 hours = 2 days 2 hours
Therefore, 2 days 2 hours from Sunday noon = 2 p.m on Tuesday.