Quantitative Aptitude · Reasoning

Time and Clocks

491 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 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.

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 $=\left( { 90 }^{ 0 }-\left( { 60 }^{ 0 }+{ 7.5 }^{ 0 } \right)  \right) ={ 22.5 }^{ 0 }$
Multiple choice physics heat energy transfers heat energy heat, internal energy and work internal energy

In a sports meet the timing of a $200\ m$ straight dash is recorded at the finish point by starting an accurate stop watch on hearing the sound of starting gun fired at the starting point. The time recorded will be more accurate

  1. In winter

  2. In summer

  3. In all seasons

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

The velocity of sound is directly proportional to the square root of absolute temperature.
The formula for velocity of sound in a gas is
$v = \sqrt {\dfrac {\gamma p}{\rho}}$
According to standard gas equation
$pV = RT$
or $p = \dfrac {RT}{V}$
$\therefore v = \sqrt {\dfrac {\gamma RT}{\rho \times V}} = \sqrt {\dfrac {\gamma RT}{M}}$
where $\rho \times V = M$, the molecular weight of the gas
$\therefore v\propto \sqrt {T}$
Hence, the sound of the gun fired at the starting point will reach the finishing point quicker in summer than in winter. The lapse of time due to the time taken by the sound in reaching the finish point will be less in summer and, hence the time recorded will be more accurate in summer than in winter.

Multiple choice free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

A watch becomes fast by 5 minutes in a day. In the watch makers shop, it keeps correct time. It is due to :

  1. natural vibrations

  2. forced vibrations

  3. damped vibrations

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

In watchmakers' shop watch is oscillated with forced vibrations, so it has keeps correct time there. By itself, watch performs oscillations at natural frequency which is faster.