Quantitative Aptitude

Clocks and Calendars

428 Questions
All Angle between hands 150 Clock gaining or losing time 132 Clock hands coincidence 69 Right angle times 30 Find time from angle 21 Decoding mixed date formats 7 Find day using reference date 6 Repeating same calendar 6 Date without reference day 3

Clocks and Calendars Questions

Multiple choice

The minute hand of a clock overtakes the hour hand at intervals of 63 minutes of the correct time. How much does the clock gain or lose?

  1. 27/11

  2. 540/77

  3. 1440/143

  4. 65/11

  5. 470/77
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

It is a correct answer. Solution : In a correct clock, the minute hand gains 55 min, over the hour hand in 60 min. To be together again,the minute hand must gain 60 minutes over the hour hand. 55min are gained in = 720/11 min But they are together after 63 min. Therefore, Gain in 63 min = (720/11)-63 = 27/11 min. Gain in 24 hours = (27/11) * 60 * 24/63 = 540/77 min.

Multiple choice

What is the angle between the two hands of a clock when time is 8:30

  1. 75(approx)

  2. 70(approx)

  3. 65(approx)

  4. 50(approx)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

At 8:30, the hour hand is halfway between 8 and 9 (at 255 degrees from 12), and the minute hand is at 6 (180 degrees from 12). The angle between them is 255-180=75 degrees. This is because the hour hand moves 30 degrees per hour plus 0.5 degrees per minute.

Multiple choice

Find the angle traced between the hour hand and the minute hand of the clock when the time is 3.25.

  1. 205/20

  2. 1500

  3. 95/20

  4. 500

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Angle traced by hour hand in 12 hour = 360 degree

Angle traced by it in 3.25 hrs = (360/12 * 41/12) degree = 205/2 degree

Angle traced by min hand in 60 min = 360 degree

Angle traced by it in 25 min = (360 * 25 / 60)degree = 150 degree

Required angle = (150 - 205/2) = 95/2 degree

Multiple choice conversion of time time conversion time measurement of time maths

A clock gains 5 minutes every hour.Then the angle traversed by the seconds hand in one minute will be 

  1. $390^0$
  2. $380^0$
  3. $360.5^0$
  4. $360^0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gain in 60 min=5min
in 1 min =$\dfrac{5}{60}min=\dfrac{5}{60}\times 60 sec=5 sec$
Angle traversed by second hand=$360^0+\dfrac{5}{60}\times 360^0=390^0$

Multiple choice conversion of time time conversion time measurement of time maths
At what time between  $1.30\mathrm { pm }$  and $2\mathrm { pm }$  will both the hands of a clock be at right angles?
  1. $4 \dfrac { 6 } { 11 }$
  2. $61 \dfrac { 5 } { 11 }$
  3. $\operatorname { Both } ( A ) \& ( B )$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The angle between $2$ successive numbers in the clock is $\dfrac{360}{12}=30^{\circ}$

The angle between successive dots is $\dfrac{360}{60}=6^{\circ}$
For one rotation of minutes hand hours hand rotates by $30^{\circ}$
$\implies $ For increase in $1$ minute there is increase of $\dfrac{1}{2}^{\circ}$ for hours hand

At $1.50\text{pm}$
Angle Between hands of clock at $90+\dfrac{50}{2}=115$

For every $1$ min there is a decrease of $\dfrac{11}{2}^{\circ}$

For every $x$ min there is a decrease of $25^{\circ}$

$\implies x=\dfrac{25\times 2}{11}=4\dfrac{6}{11}$min

So at $4\dfrac{6}{11}$ pm the hands are perpendicular to each other.

Multiple choice lorentz transformation and muon experiment option a: relativity physics

The minute hand of the clock is 4 cm long. The average velocity of the tip of the minute hand between 11:00 am to 11:30 am is:

  1. $1.5\times { 10 }^{ -5 }{ m }/{ s }$
  2. $4.4\times { 10 }^{ -5 }{ m }/{ s }$
  3. $1.8\times { 10 }^{ -6 }{ m }/{ s }$
  4. $3.5\times { 10 }^{ -6 }{ m }/{ s }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average velocity $ = \dfrac{Total \; Displacement}{Total \; Time}$


$ = \dfrac{  2\times 0.04}{30 \times 60} = 4.44 \times 10^{-5} \;m/s$

Multiple choice lorentz transformation and muon experiment option a: relativity physics
Two clocks are running in synchronism. One clock is moved at a very high speed and returned to the original position on the earth while the other remains at rest. The time passed in the travelling clock is 1 hr. Which of the following could be the time passed in the clock kept on the earth.

  1. 30 minutes

  2. 45 minutes

  3. 59 minutes

  4. 1 hours

  5. 2 hours
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

According to the time dilation concept of relativity, the moving clock runs at slower rate than the rest clock  i.e rest clock measures longer time taken by an event than the moving clock.

Hence time elapsed in the clock kept on earth must be greater than 1 hr.
So, option E is correct.

Multiple choice evs magic with mirrors lateral inversion right or left reflection at plane surface

A clock fixed on a wall shows time 04 : 25 : 37. Its image in a plane mirror shows :

  1. 07 : 30 : 33

  2. 07 : 43 : 32

  3. 07 : 35 : 22

  4. 43 : 27 : 36
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

After reflection,
Image of the hour hand will look like its pointing between 7 and 8.
Image of the minute hand will look like its pointing at 7.
Image of the hour hand will look like its pointing between 4 and 5.
So the time will appear to be $07 : 35 : 22$

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At 5'O clock the angle between two hands in a clock is 

  1. ${ 120 }^{ \circ }$
  2. ${ 130 }^{ \circ }$
  3. ${ 140 }^{ \circ }$
  4. ${ 150 }^{ \circ }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
A clock has $12$ equal parts$={360}^{\circ}$
$1$ part$=\dfrac{{360}^{\circ}}{12}={30}^{\circ}$
At $5$O clock the hands will be between $12$ and $5=5$parts
$\therefore 5$ parts$=5\times{30}^{\circ}={150}^{\circ}$
Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

The centre of a clock is taken as origin At 4.30 pm the equation of line along minute hand is x = 0 Therefore at this istant the equation of line along the hour hand will be 

  1. $x - y = 0$
  2. $x + y = 0$
  3. $\displaystyle y=\sqrt{2x}$
  4. $\displaystyle y=\frac{x}{\sqrt{2}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The centre of a clock is taken as origin. At 4:30 pm equation of line along minute hand is $x=0$.
Therefore at this instant the equation of line along the hour hand will be 
$m=-1$ ( as tan 135=-1 )
Therefore equation of line y=mx
or $y=-x$
$y+x=0$.

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At 4.24 pm, how many degrees has the hour hand of a clock moved from its position at noon?

  1. $132^\circ$
  2. $135^\circ$
  3. $140^\circ$
  4. $145^\circ$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

From noon 12 noon to 4:24 total minutes
4*60+24
=240+24
=264
Now in 12 hour angle made by the hour hand= $={ 360^0 } $
so in 1 minute angle made by the hour hand=360/12*60=$= { \frac { 1 }{ 2 }  } $
so in 264 minute angle made by the hour hand=$=264\times \frac { 1 }{ 2 } ={ 132^0 } $

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

The minute hand of a clock is 14 cm long
How much distance dose the end of the minute hand
travel in 15 minutes?$\displaystyle \left ( Take \pi  =\frac{22}{7}\right )$

  1. 11 cm

  2. 22 cm

  3. 33 cm

  4. 44 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given minute hand of clock is 14 cm long

Then distance traveled by minute hand in 15 minutes
= one forth of circumference of circle radius 14 cm
=$\left ( \frac{1}{4}\times 2\times \frac{22}{7}\times 14 \right )=22 cm$

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At 5:20 the angle formed between the two hands of a clock is

  1. obtuse

  2. right

  3. acute

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A clock is a circle, and a circle always contains $360^o$. Since there are 


$60$ minutes on a clock, each minute mark is $6^o.$

$\Rightarrow$  $\dfrac{360^o}{60}=6\,degree$
The minute hand on the clock will point at $20$ minutes, allowing us to calculate it's position on the circle.

$\Rightarrow$  $20\,minutes\times 6=120\,degree$
So the angle made by the hour hand in $5$ hours $20$ minutes $= 5\dfrac{1}{3}hours$ 
                                                                                                    $=\dfrac{16}{3}\times\dfrac {360^o}{12}$ 
                                                                                                    $=160^o$

Hence angle between the hour hand and minute hand at $5:20=160^o-120^o=40^o$

$\therefore$  $40^o$ is less than $90^o$ means its acute angle.

$\therefore$   At $5:20$ the angle formed between the two hands of a clock is $acute.$

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At 3 o'clock, the angle formed between the two hands of a clock is

  1. right

  2. acute

  3. obtuse

  4. left
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  A clock is a circle made of $360^o$. and that 

$\Rightarrow$  Each number represents an angle and the separation between them is $\dfrac{360}{12}=30^o$. 
$\Rightarrow$  At $2:00$, the minute hand is on the $12$ and the hour hand is on the $3$.  
$\Rightarrow$  The angle between two hands $=3\times 30^o=90^o$
$\Rightarrow$  At $3$ o'clock, the angle formed between the two hands of a clock is $right\,angle.$