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

What friction of a clockwise revolution does the hour hand of a clock turn through, when it goes from

  1. $3$ to $9$
  2. $4$ to $7$
  3. $7$ to $10$
  4. $12$ to $9$
  5. $1$ to $10$
  6. $6$ to $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let us consider that for one hour the fraction of revolution is $\dfrac{1}{12}$

then :

(i)  $3$ to $9$ means $6$ hours

therefore; fraction of revolution $\dfrac{6}{12}=\dfrac{1}{2}$

(ii)  $4$ to $7$ means $3$ hours

therefore; fraction of revolution $\dfrac{3}{12}=\dfrac{1}{4}$  

(iii)  $7$ to $10$ means $3$ hours

therefore; fraction of revolution $\dfrac{3}{12}=\dfrac{1}{4}$

(iv)  $12$ to $9$ means $9$ hours

therefore; fraction of revolution $\dfrac{9}{12}=\dfrac{3}{4}$

(v)  $1$ to $10$ means $9$ hours

therefore; fraction of revolution $\dfrac{9}{12}=\dfrac{3}{4}$

(vi)  $6$ to $3$ means $9$ hours

therefore; fraction of revolution $\dfrac{9}{12}=\dfrac{3}{4}$

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 angle between the minute hand and the hour hand of a clock when the time is 3:30 in degree is

  1. 90

  2. 09

  3. 88

  4. 75
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Angular speed of hour hand $= 30degree \,per\, hour. =0.5$ degree/minute.

In $30$ minutes , the angle swept by hour hand is $30\times 0.5 = 15$ degree.

At $3:30$ , the minute hand is at number $6$.

At $3:00$ the hour hand was at number $3$.

Now it has moved $15$ degree.

Hence the angle between the two is $\left(90 -15\right) = 75$ degree.
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 angle between the minute hand and the hour hand of a clock when the time is 4:20 in degree is:

  1. 20

  2. 30

  3. 10

  4. 80
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The speed of hour hand is ( $30$ degree per hour) ${0.5}^{\circ}$ per minute.

The speed of minute hand is ($360$ degree per hour) ${6}^{\circ}$ per minute.

Relative to hour hand the speed of minute hand is $6-0.5 = {5.5}^{\circ}$per minute.

At $4$ O clock , hour hand is at $4$ and minute hand is at $12$.

Angle between them is ${120}^{\circ}$.

Keeping hour hand at $4$ , minute hand moves $20\times 5.5 = {110}^{\circ}$, in $20$ minutes.

Angle between them is ${120}^{\circ}-{110}^{\circ}={10}^{\circ}$.

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

At what time between 4 and 5, will the hands of a clock coincide?

  1. 15.81 min

  2. 21.81min

  3. 23.81 min

  4. 33.48 min
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
We know minute hand of a clock covers ${360}^{\circ}$ in $60\ min$ or ${6}^{\circ}$ in $1$ minute and hour hand of a clock covers ${360}^{\circ}$ in $12\ hrs$ or ${30}^{\circ}$ in $1$ hour or $.5$ degree in $1$ min.

So at $4:00$ the minute hand has covered $0$ degrees and hour hand has covered $120$ degrees

Now let time after which these two coincide be $x$ min.

So hour hand covers $120+\dfrac{x}{2}$ upto that time and minute hand covers $6x$ degrees upto that time when they coincide the angles should be same

So, $120+\dfrac{x}{2}= 6x$

Solving we get $6x-\dfrac{x}{2}=120$

$\Rightarrow\,\dfrac{12x-x}{2}=120$

$\Rightarrow\,11x=240$

$\Rightarrow\,x=\dfrac{240}{11}$minutes

$\therefore\,x=21.81\ mins$
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

Angle between the minutes hand of a clock and hour hand when the time is 7 : 20 am is 

  1. $\displaystyle 80^{\circ}$
  2. $\displaystyle 100^{\circ}$
  3. $\displaystyle 120^{\circ}$
  4. $\displaystyle 140^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At 7:20, the minute hand is at 4 (20 minutes). The hour hand has moved past 7 by 20/60 of the way to 8. Hour hand position = 7 + 20/60 = 7.33. Angle = |(30 * 7.33) - (6 * 20)| = |220 - 120| = 100 degrees.

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

What is the angle (in circular measure) between the hour hand and the minute hand of a clock when the time is half past $4$?

  1. $\dfrac{\pi}{3}$
  2. $\dfrac{\pi}{4}$
  3. $\dfrac{\pi}{6}$

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In the clock the angle between each hour division will be $\dfrac { 360 }{ 12 } =30^{o}$. 

Now here at $4:30$, the hour hand will be along AB which is the angle bisector between $4$ and $5$ and the minute hand will be along AC,
The angle between them will be $=30+15=45$,in radians $\dfrac { \pi  }{ 4 }$ 

Hence, B is correct.

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 what time is the angle between the hands of a clock equal to $30^{o}$ ?

  1. $1:00$
  2. $11:00$
  3. $2:00$
  4. $12:00$
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

A clock is a circle made of $360^\circ$, and that each hour represents an angle and the separation between them is $\dfrac{360^\circ}{12}=30^\circ$


Hence, 
At $1:00$ the angle between the hands is $30^\circ$, minute hand pointing at 12 and hour hand at 1.

Similarly
At $11:00$ the angle between the hands is $30^\circ$

At $2:00$ the angle between the hands is $60^\circ$

At $12:00$ the angle between the hands is $0^\circ$

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

How many times between $6:00$ am and $6:00$ pm, do the hands of a clock make a straight line 

  1. $9$
  2. $10$
  3. $11$
  4. $12$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours.

 (Because between 5 and 7 they point in opposite directions at 6 o'clock only).

So between $6:00$ am to $6:00$ pm ($12$ hours), $11$ times hands of a clock make a straight line.
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

How many times in a day, do the hands of a clock make a right angle ?

  1. $21$
  2. $22$
  3. $42$
  4. $44$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

There will be $2$ times per hour when the angle between minute and hour hand is $90^\circ$

Total of $22$ times in $12$ hours.
$\therefore$ In $24$ hours, $22\times 2=44$ times the angle between minute and hour hand is $90^\circ$.

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

At 2:15 o'clock, the hour and minute hands of a clock form an angle of:

  1. $30^{\circ}$
  2. $5^{\circ}$
  3. $22\dfrac{1}{2}{\circ}$
  4. $7\dfrac{1}{2}{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
   $\underset { \downarrow  }{ \underline { 2 }  } <2:15<\underset { \downarrow  }{ 3 } $' $O$ clock
$\left( { 60 }^{ 0 } \right) $             $\left( { 90 }^{ 0 } \right) $
when minute hand rotates $15$ min hour hand rotate $\dfrac { 15 }{ 60 } \times { 30 }^{ 0 }={ 7.5 }^{ 0 }$
So, angle at $2:15$ is $=\left( { 90 }^{ 0 }-\left( { 60 }^{ 0 }+{ 7.5 }^{ 0 } \right)  \right) ={ 22.5 }^{ 0 }$