Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making

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LR : Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

The document Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev is a part of the LR Course UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making.
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1. An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

A. 154°

B. 180°

C. 170°

D. 160°

 

Answer: Option B

Explanation:

We know that angle traced by hour hand in 12 hrs = 360°

From 8 to 2, there are 6 hours.

Angle traced by the hour hand in 6 hours =  Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

 

2. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through

A. 155°

B. 145°

C. 152°

D. 140°

 

Answer: Option A

Explanation:

We know that angle traced by hour hand in 12 hrs = 360° 

Time duration from noon to 10 minutes past 5
Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

Hence the angle traced by hour hand from noon to 10 minutes past 5

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

 

 

3. At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but not together?

A. 5 minutes past 7

B.  Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev  minutes past 7

C.  Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev  minutes past 7

D. Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev minutes past 7

 

Answer: Option D

Explanation:

Solution 1

The two hands of a clock will be in the same straight line but not together between H and (H+1) o' clock at

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

 

Here H = 7. 

Hands of the clock will point in opposite directions at

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev  minutes past 7

= Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev  minutes past 7

= Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev  minutes past 7 

=Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev minutes past 7

 

Solution 2

It's better to use formula as it can save lots of time in exams. However we should understand the basics for sure. Please find the method given below to solve the same problem in the traditional way.

If the hands of the clock are in the same straight line, but not together, they will be 30 minute spaces apart.

At 7'o clock, the hands of the clock are 25 minute spaces apart. Hence the minute hand should gain 5 minute spaces over the hour hand so that the hands will be 30 minute spaces apart.

In 60 minutes, minute hand gains 55 minute spaces over the hour hand.

Hence, to gain 5 minute spaces for the minute hand, time needed

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

That means when the time is Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev minutes past 7, the hands of a clock will be in the same straight line but not together.

 

4. At what time between 5.30 and 6 will the hands of a clock be at right angles?

A. 44 minutes past 5

B. Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev minutes past 5

C. Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev minutes past 5

D. 43 minutes past 5

 

 

Answer: Option C

Explanation:

Solution 1

The two hands of the clock will be at right angles between H and (H+1) o' clock at
Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev  minutes past H 'o clock

Let's see the times at which right angles are formed between 5 and 6

Let's take H=5. Hence the two hands will be at right angles between 5 and 6 at

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev  minutes past 5 comes before 5.30.  Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev minutes past 5 comes between 5.30 and 6. The question is to find out the time between 5.30 and 6 when the hands of a clock will be at right angles. Hence the required time is Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev minutes past 5

 

Solution 2
 

At 5, the hands are 25 minutes spaces apart.

To get a right angle when the time is between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 minute spaces over the hour hand.

In 60 minutes, minute hand gains 55 minute spaces over the hour hand.

Hence, to gain 40 minute spaces for the minute hand, time needed 
Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRevClocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

That means when the time is  Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev  minutes past 5, the hands of a clock will be at right angles

 

5. At what angle the hands of a clock are inclined at 15 minutes past 5?

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

Answer: Option A

Explanation:

Solution 1
 

Angle between hands of a clock 

When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

Here H = 5, M = 15 and the minute hand is behind the hour hand. 

Hence the angle

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

 

Solution 2
 

15 minutes past 5 
= 5 hour 15 minutes 
Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

Angle traced by hour hand in 12 hours = 360°

Hence angle traced by hour hand in  Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev hour
Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

Required angle = 157.5 - 90 = 67.5°

 

6. At 3:40, the hour hand and the minute hand of a clock form an angle of

A. 135°

B. 130°

C. 120°

D. 125°

 

Answer: Option B

Explanation:

Solution 1

 

Angle between hands of a clock 

When the minute hand is behind the hour hand, the angle between the two hands at MM minutes past HH 'o clock
Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

When the minute hand is ahead of the hour hand, the angle between the two hands at MM minutes past HH 'o clockClocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

Here H = 3, M = 40 and minute hand is ahead of the hour hand. 

Hence the angle

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

 

Solution 2
Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

Clocks - Examples (with Solutions), Logical Reasoning LR Notes | EduRev

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