Clocks -Fundamental Principles

Tuesday, February 19th, 2013


CLOCKS – FUNDAMENTAL PRINCIPLES

 

Questions on clocks (or even calendars) are not really frequent in CAT these days. They used to be really popular few years ago. Having said that, it is always better to understand some of the basic principles and the types of problems that get asked. They might come in handy in case of other exams like CMAT, MAT, SNAP, etc.

 

Clock problems can be broadly classified in two categories:

a)      Problems on angles

b)      Problems on incorrect clocks

 

Problems on angles

Before we actually start solving problems on angles, we need to get couple of basic facts clear:

 

The questions based upon these could be of the following types

 

Example 1: What is the angle between the hands of the clock at 7:20

At 7 o’ clock, the hour hand is at 210 degrees from the vertical.

In 20 minutes,

Hour hand = 210 + 20*(0.5) = 210 + 10 = 220 {The hour hand moves at 0.5 dpm}

Minute hand = 20*(6) = 120                       {The minute hand moves at 6 dpm}

Difference or angle between the hands = 220 – 120 = 100 degrees

 

Example 2: At what time do the hands of the clock meet between 7:00 and 8:00

Ans: At 7 o’ clock, the hour hand is at 210 degrees from the vertical.

In ‘t’ minutes

Hour hand = 210 + 0.5t

Minute hand = 6t

They should be meeting each other, so

210 + 0.5t = 6t

Hands of the clock meet at 7 : 38 : 2/11th

 

Example 3: At what time do the hands of a clock between 7:00 and 8:00 form 90 degrees?

Ans: At 7 o’ clock, the hour hand is at 210 degrees from the vertical.

In ‘t’ minutes

Hour hand = 210 + 0.5t

Minute hand = 6t

The difference between them should be 90 degrees. Please note that it can be both before the meeting or after the meeting. You will get two answers in this case, one when hour hand is ahead and the other one when the minute hand is ahead.

Case 1: 210 + 0.5t – 6t = 90

Case 2: 6t – (210 + 0.5t) = 90

 

So, the hands of the clock are at 90 degrees at the following timings:

7 : 21 : 9/11th  and 7 : 54 : 6/11th

 

Some other results which might be useful:

 

Problems on incorrect clocks

Such sort of problems arise when a clock runs faster or slower than expected pace. When solving these problems it is best to keep track of the correct clock.

 

Example 4: A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day?

Ans: The watch gains 5 seconds in 3 minutes => 100 seconds in 1 hour.

From 8 AM to 10 PM on the same day, time passed is 14 hours.

In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.

So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

 

Example 5: A watch gains 5 seconds in 3 minutes and was set right at 8 AM. If it shows 5:15 in the afternoon on the same day, what is the correct time?

Ans: The watch gains 5 seconds in 3 minutes => 1 minute in 36 minutes

From 8 AM to 5:15, the incorrect watch has moved 9 hours and 15 minutes = 555 minutes.

When the incorrect watch moves for 37 minutes, correct watch moves for 36 minutes.

I am sure you would have heard the proverb that even a broken clock is right twice a day. However, a clock which gains or loses a few minutes might not be right twice a day or even once a day. It would be right when it had gained / lost exactly 12 hours.

 

Example 6: A watch loses 5 minutes every hour and was set right at 8 AM on a Monday. When will it show the correct time again?

Ans: For the watch to show the correct time again, it should lose 12 hours.

It loses 5 minutes in 1 hour

 

I hope that this session was useful to you. If it wasn’t let me present the greatest song on clocks that has ever been written in any language – click here. (No. It is not Coldplay)

Clocks -Fundamental Principles
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