Quantitative Aptitude · Reasoning

Time and Clocks

562 Questions

Time and clocks problems evaluate quantitative aptitude by testing concepts on clock gains, losses, and relative speeds of hands. Questions also cover global time zones and standard time calculations. These logical reasoning topics frequently appear in SSC and banking exams.

Clock gain or lossTime zonesAngle between handsStandard time calculationPrecise time measurement

Time and Clocks 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

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 $right\,angle.$

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

At what time between $2$ and $3$ the acute angle between the hour hand and the minute hand will be $50^{o}$

  1. $2:20$
  2. $2:25$
  3. $2:35$
  4. $2:40$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for the angle between clock hands is |30H - 5.5M|. For 2:20, |30(2) - 5.5(20)| = |60 - 110| = 50 degrees. This matches the requirement.

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.