Calendar Remaining + Clock | Reasoning | Short Tricks By Rajesh Choudhary Sir (2020)
17Calendar Remaining + Clock | Reasoning | Short Tricks By Rajesh Choudhary SIr
A clock has two hands : Hour hand and Minute Hand . The minute hand (M.H.) is also called the long and the hour hand (H.H.) is also called the short hand.
The clock has 12 hours numbered from 1 to 12.
Also, the clock is divided into 6 equal minute divisions. Therefore, each hour number is separated by five minute divisions.
Therefore,
• One minute division = 360/60 = 6° apart . i.e. in one minute, the minute hand moves 6°.
• One hour division = 6° x 5 = 30° apart i.e. In one hour, the hour hand moves 30° apart.
• Also, in one minute, the hour hand moves
=30/60 = 1/2° apart.
• Since, in one minute, minute hand moves 6° and hour hand moves 1/2°, therefore, in one minute, the minute hand gains 5*1/2° more than hour hand.
• In one hour, the minute hand gains 5*1/2°× 60
= 330°
over the hour hand. i.e. the minute hand gains 55 minutes divisions over the hour hand.
Relative position of the hands
Any relative position of the hands of a clock is repeated 11 times in every 12 hours.
(a) When both hands are 15 minute spaces apart, they are at right angle.
(b) When they are 30 minute spaces apart, they point in opposite directions.
(c) The hands are in the same straight line when they are coincident or opposite to each other.
• In every hour, both the hand coincide once.
• In a day, the hands are coinciding 22 times.
• In every 12 hours, the hands of clock coincide 11 times.
• In every 12 hours, the hands of clock are in opposite direction 11 times.
• In every 12 hours, the hands of clock are at right angles 22 times.
• In every hour, the two hands are at right angles 2 times.
• In every hour, the two hands are in opposite direction once.
• In a day, the two hands are at right angles 44 times.
• If both the hands coincide, then they will again
coincide after 65*5/11 minutes. i.e. in correct
clock, both hand coincide at an interval of 65*5/11 minutes.
• If a watch incicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast.
On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minute too slow.
Example 1: At what time between 4 and 5 o’clock will the hands of a clock are perpendicular to each other?
Solution:
At 4 o’clock, the minute hand will be 20 min. spaces behind the hour hand. Now, when the two hands are at right angles, they are 15 min. spaces apart. So they are at right angles in following two cases.
Case I. When minute hand is 15 min. spaces behind the hour hand:
In this case min hand will have to gain (20–15) = 5 minute spaces.
5 min. spaces will be gained by it in 60/55 + 5 = 5*5/11 min
They are at right angles at 5*5/11 min. past 4.
Case II. When the minute hand is 15 min. spaces ahead of the hour hand :
To be in this position, the minute hand will have to gain (20 + 15) = 35 minute spaces.
55 min. spaces are gained in 60 min.
35 min. spaces are gained in 60/55 * 35 = 38*2/11 min
They are a right angles at 38*2/11 past 4.