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Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

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1. An accurate clock shows 8 o'clock in the morning. Through how many 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 based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

 

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 based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC
Hence the angle traced by hour hand from noon to 10 minutes past 5

Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

 

 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 based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC  minutes past 7

C.  Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC  minutes past 7

D. Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC 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 based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

Here H = 7.
Hands of the clock will point in opposite directions at Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC  minutes past 7
= Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC  minutes past 7
= Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC  minutes past 7
=Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC 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, the minute hand gains 55-minute spaces over the hour hand.
Hence, to gain 5-minute spaces for the minute hand, the time needed

Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

That means when the time is Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC 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 based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC minutes past 5

C. Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC 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 based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC  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 based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC  minutes past 5 comes before 5.30.  Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC 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 based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC 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, the minute hand gains 55-minute spaces over the hour hand.
Hence, to gain 40-minute spaces for the minute hand, the time needed
Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSCClocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC
That means when the time is  Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC  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 based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

Answer: Option A

Explanation:

Solution 1

The 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 based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

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

Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

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

Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

 

Solution 2

15 minutes past 5
= 5 hour 15 minutes
Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC
Angle traced by hour hand in 12 hours = 360°
Hence angle traced by hour hand in  Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC hour
Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC
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

 The 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 based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC
When the minute hand is ahead of the hour hand, the angle between the two hands at MM minutes past HH 'o clockClocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

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

Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

 

Solution 2
Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

Clocks based Questions - Notes | Study CSAT Preparation for UPSC CSE - UPSC

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