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__Clocks Aptitude Important Formulas, tricks and shortcut Methods:__

__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.

__Example: 01__**At what time between 2’O clock and 3’O clock, the hands of the clock are opposite to each other?**

__Solution:__
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.

__Example: 02__**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?**

__Solution:__
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.

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