# Clocks Questions for Aptitude YouTube Lecture Handouts for CDS Exam

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## Clocks

## Saying Time

Saying time

How to tell the time so, the time is the most of the aptitude problem not given directly they would write in the numerals i.e.. 1: 00 (1 O′clock or 1 hour 00 minute)

Similarly, all the times till 30 minutes are representing in terms of PAST for example five past one, quarter past 1 means 1: 15

After half past which means, after 1: 30

We can say how many minutes left before we reach TO.

For example, 1: 45 instead of in terms of quarter-to TO which means 15 minutes are left before we reach 2 O′clock.

There are two another important concepts: Top of the hour and Bottom of the hour

Top of the hour it means the minute hand in at 12 and bottom of the hour it means the minute hand at 6 and 30 minutes past the hours.

## Race of Hands (Relative Speed of Clock Hands)

How the two hands moving in the clock in the speed?

Speed in hour:

Degrees are covered in hour is 1 minute.

Speed in minute:

Relative Speed:

## Clock Related Aptitude Problems

The track is the phase of the clock off course racers to be the two hands of the clock.

## Angles in a Clock

In given, we can say here 2 o′clock, the hour hand moves by

The other angle is smaller angle which is travel in minutes. That means smaller angle

For example: how to represent 2: 20

How to write? The shorter hand is within the boundary of clock and minute hand or longer hand is offside the boundary of clock.

For example: 2: 20

Angle between the hour hand the minute hand

Minute hand covered angle

So,

What the angle of 12 O′clock line to minute hand?

So, angle between 12 O′clock line to minute hand

Angle between hour hand and minute hand

Therefore, reflection angle

## Relation between Time and Angle

The ratio of hour and minute means time and angle -

Given formula is very important.

By how many degrees does hour hand rotate from 8 in the morning to 2 in afternoon?

In given question,

8 o′clock in the morning and 2 o′clock in afternoon

Hour between 8 to 2

Each hour

Total degree

## Angle when Time is 2: 20 and 2: 20 ⁄ 11 Min

There are two times 2: 20 and 2: 20 ⁄ 11 min, find the angle between these two times.

Hour , minute

Negative value comes then it discards that.

Hour , minute

Time between 2 & 3 when angle is 50 degrees?

Hour

Minute

When you remove the absolute sign into bracket

Put the in here

Put then

Put then the

So,

## Special Cases: Coincidence (Zero Degree)

What happen when 12 o′clock?

That means hand of the clock would be together at 11: 60, similar at 12 o′clock

So, times of the hand of clock in coincidence.

## Special Cases: Opposite (180 Degree)

At what time after 4: 00, the hour and the minute hand will lie opposite to each other?

What happen between 4 o′clock and 5 o′clock

Only one value at one time so, that is

times in 12 hours

## Special Cases: Right Angles (90 Degrees)

2: 60 at 3 o′clock in one time similarly 8: 60 at 9 o′clock at one time

24 such configuration the hands are in 12 hr period at 22 such positions

And 24 hours period at

## General Case: Say 30 Degrees

1 o′clock at the angle between

After how much time the configuration is repeats, it covers relatively to

It solve that,

Then, in 12 hour period

Two possibilities to repeat minute hand so, in 12 hours period

## Variations

- Crossing vs. overlap
- Overlap vs. opposite vs. straight

Overlap happens exactly the top of the hand and crossing happens at little be later

Overlap happens at 11 times in 12 hours period, hands of opposite is also 11 times and straight either overlap or opposite in both case so, straight line is 22 times in 12 hours period

## At What Time between 4 and 5 O′Clock Will the Minute-Hand of a Watch be 13 Minutes in Advance of the Hour Hand?

The minute-hand of a watch be 13 minutes at

## Next Class: Complicated Problems

- When would three hands of a clock all overlap?
- It is now past 3 o′clock in the afternoon. The minute hand is 3 minutes from now will be directly opposite the hour hand 9 minutes ago. What is the time now?
- A clock is operating normally. It is now sometime between 7: 00 and 8: 00. In less than one hour, the minute hand and the hour hand will have exactly exchanged positions. Find the number of minutes after 7: 00 that the time is now.
- An absent-minded watch repairman connected the hour hand to the minute hand pinion and the minute hand to the hour hand pinion and set the clock at 6 AM which was the correct time then. How soon after 6 AM will this clock give the correct time again? How many times during the day would clock show correct time?
- In a clock with identical dials for hours and minutes, how many times a day you can՚t tell the time?

-Mayank