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Clocks based Questions | Quantitative Aptitude (Quant) - CAT PDF Download

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 | Quantitative Aptitude (Quant) - CAT

 

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 | Quantitative Aptitude (Quant) - CAT
Hence the angle traced by hour hand from noon to 10 minutes past 5

Clocks based Questions | Quantitative Aptitude (Quant) - CAT

 

 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 | Quantitative Aptitude (Quant) - CAT  minutes past 7

C.  Clocks based Questions | Quantitative Aptitude (Quant) - CAT  minutes past 7

D. Clocks based Questions | Quantitative Aptitude (Quant) - CAT 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 | Quantitative Aptitude (Quant) - CAT

Here H = 7.
Hands of the clock will point in opposite directions at Clocks based Questions | Quantitative Aptitude (Quant) - CAT  minutes past 7
= Clocks based Questions | Quantitative Aptitude (Quant) - CAT  minutes past 7
= Clocks based Questions | Quantitative Aptitude (Quant) - CAT  minutes past 7
=Clocks based Questions | Quantitative Aptitude (Quant) - CAT 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 | Quantitative Aptitude (Quant) - CAT

That means when the time is Clocks based Questions | Quantitative Aptitude (Quant) - CAT 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 | Quantitative Aptitude (Quant) - CAT minutes past 5

C. Clocks based Questions | Quantitative Aptitude (Quant) - CAT 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 | Quantitative Aptitude (Quant) - CAT  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 | Quantitative Aptitude (Quant) - CAT

Clocks based Questions | Quantitative Aptitude (Quant) - CAT  minutes past 5 comes before 5.30.  Clocks based Questions | Quantitative Aptitude (Quant) - CAT 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 | Quantitative Aptitude (Quant) - CAT 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 | Quantitative Aptitude (Quant) - CATClocks based Questions | Quantitative Aptitude (Quant) - CAT
That means when the time is  Clocks based Questions | Quantitative Aptitude (Quant) - CAT  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 | Quantitative Aptitude (Quant) - CAT

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 | Quantitative Aptitude (Quant) - CAT

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 | Quantitative Aptitude (Quant) - CAT

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

Clocks based Questions | Quantitative Aptitude (Quant) - CAT

 

Solution 2

15 minutes past 5
= 5 hour 15 minutes
Clocks based Questions | Quantitative Aptitude (Quant) - CAT
Angle traced by hour hand in 12 hours = 360°
Hence angle traced by hour hand in  Clocks based Questions | Quantitative Aptitude (Quant) - CAT hour
Clocks based Questions | Quantitative Aptitude (Quant) - CAT
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 | Quantitative Aptitude (Quant) - CAT
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 | Quantitative Aptitude (Quant) - CAT

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

Clocks based Questions | Quantitative Aptitude (Quant) - CAT

 

Solution 2
Clocks based Questions | Quantitative Aptitude (Quant) - CAT

Clocks based Questions | Quantitative Aptitude (Quant) - CAT

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FAQs on Clocks based Questions - Quantitative Aptitude (Quant) - CAT

1. What is the history of clocks?
Ans. Clocks have a long history dating back thousands of years. The first mechanical clocks were developed in ancient Egypt and ancient China around 2000 BCE. These early clocks were based on the movement of the Sun, stars, and water. Over time, clocks evolved with the invention of various mechanisms, such as pendulums and escapements, leading to the development of more accurate timekeeping devices.
2. How do mechanical clocks work?
Ans. Mechanical clocks work by using a series of gears and springs to translate the energy from a wound-up spring into the movement of the clock's hands. The key components of a mechanical clock include the mainspring, gears, escapement, and pendulum (if present). The mainspring provides the energy, which is then transferred through the gears to control the speed at which the hands move. The escapement regulates this movement, while the pendulum helps maintain the clock's accuracy.
3. What are the different types of clocks?
Ans. There are several different types of clocks, including mechanical clocks, digital clocks, analog clocks, and atomic clocks. Mechanical clocks, as mentioned earlier, rely on mechanical components to keep time. Digital clocks display time in numerical format using electronic circuits. Analog clocks feature hour and minute hands on a dial, while atomic clocks use the vibrations of atoms to maintain extreme accuracy.
4. How accurate are atomic clocks?
Ans. Atomic clocks are the most accurate timekeeping devices available. They are accurate to within a few billionths of a second per day. Atomic clocks measure time based on the vibrations of atoms, typically using cesium or rubidium atoms. These clocks are used as standards for timekeeping worldwide and are crucial for various applications such as satellite navigation systems, telecommunications networks, and scientific research.
5. Can clocks be affected by changes in altitude or temperature?
Ans. Yes, clocks can be affected by changes in altitude and temperature. Mechanical clocks, especially those with pendulums, can experience changes in their timekeeping accuracy when exposed to different altitudes or temperatures. This is because the length of a pendulum can be affected by changes in gravity due to altitude, and the expansion or contraction of materials can affect the movement of gears. Modern electronic clocks and atomic clocks are designed to minimize these effects and maintain accuracy regardless of environmental conditions.
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