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 how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

Gabriel watched $3$ old movies on videotape. The first movie was $62$ minutes long. The
second was $1$ hour $34$ minutes long. The third was $1$ hour $25$ minutes long. He started
watching at $3:15$ P.M. At what time did the last movie end?

  1. $7:00$ P.M.
  2. $7:08$ P.M.
  3. $7:12$ P.M.
  4. $7:16$ P.M.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First movie $62$ min.

Second movie $94$ min
Third movie $85$ min
so total time of movie will be $241$ minutes
which makes $4$ hours and 1 minute
So he should finish $3:15 + 4:01$ = $7:16 $ P.M.

Multiple choice physics units and measurement: error analysis accuracy of measurement accuracy and precision accuracy, precision and uncertainty in measurement

Which of the following time measuring devices is most precise?

  1. A wall clock

  2. An atomic clock

  3. A digital watch

  4. stop watch
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Option $(B)$ is correct because a clock can measure time correctly up to one second. A stopwatch can measure time correctly up to a fraction of a second. A digital watch can measure time up to a fraction of second whereas an atomic clock is the most accurate timekeeper and is based on characteristic frequencies of radiation emitted by certain atoms having a precision of about $1$ second in $300,000$ years. So an atomic clock can measure time most precisely as the precision of this clock is about $1 s$ in $10^{13} s$.

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 $right\,angle.$

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

Let $A$ be the angle between the minute and the hour hand at $6$ p.m. and $B$ be the angle between them at $12$ a.m. Then which of the following statements is true?

  1. $A < B$
  2. $A > B$
  3. $A=B$

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

At 6 p.m., the minute hand points at 12 and the hour hand points at 6, forming a straight line, which is an angle of 180 degrees (A = 180). At 12 a.m., both the minute and hour hands coincide at 12, forming an angle of 0 degrees (B = 0). Therefore, A is greater than B.

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 $\dfrac{9}{12}=\dfrac{3}{4}$