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 measuring time time in 24 hour clock time difference time

A clock runs 6 minutes slow per day. By what percentage is it running slow?

  1. 6

  2. 1/10

  3. 12/5

  4. 5/12

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

$The\quad clock\quad is\quad running\quad 6\quad minutes\quad slow\quad in\quad 1\quad day,\ %\quad of\quad time\quad lost=\frac { 6 }{ 24*60 } *100=\frac { 5 }{ 12 }%$

Multiple choice maths measuring time time in 24 hour clock time difference time

What is the angle between the $2$ hands of the clock at $8:24$ pm?

  1. $\displaystyle 100^{\circ}$
  2. $\displaystyle 107^{\circ}$
  3. $\displaystyle 106^{\circ}$
  4. $\displaystyle 108^{\circ}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Required angle = 240 - 24 $\displaystyle \times $ (11/2)
                        = 240 - 132 = $\displaystyle 108^{\circ}$

Multiple choice maths measuring time time in 24 hour clock time difference time

At what angle are the hands of a clock inclined at $30$ minutes past $6 $?

  1. $7\displaystyle\frac{1}{2}$
  2. $11\displaystyle\frac{1}{2}$
  3. $15$
  4. $23$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Angle between hands of clock $=\left| 30H- \displaystyle\frac { 11 }{ 2 } M \right| $
where $H \rightarrow $ Hour hand, $M \rightarrow $ Minute hand
$\therefore  \left| 30\times 6- \displaystyle\frac { 11 }{ 2 } \times 30 \right| =15$

Multiple choice maths measuring time time in 24 hour clock time difference time

There are two clocks on a wall, both set right at 10:00 a.m. on Sunday. Both the clocks lose 1 minute and 2 minute, respectively, every hour. Ifthe clock which loses 2 minutes every hour shows 8:00 p.m. on the following Tuesday, what time does the clock which loses 1 minute every hour show?

  1. 8:30 p.m.

  2. 9:00 p.m.

  3. 8:45 p.m.

  4. 9:30 p.m.

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

Let the hours passed be x,
time shown on clock 1=8:00 p.m. tuesday (24+24+10 hrs)
60x-2x=58*60,
x=60hrs,
actual time=10:00 p.m.
time on clock 2=(60-1)*60=59hrs,
=9:00 p.m. tuesday.

Multiple choice maths measuring time time in 24 hour clock time difference time

From $6$ am to $6$ pm, the number of times the angle between the two hands of a clock is $\displaystyle { 180 }^{ o }$ is 

  1. $2$
  2. $11$
  3. $13$
  4. $14$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The two hands of a clock make $\displaystyle { 180 }^{ o }$ when they face each other in a straight line. 
This happens 11 times in 12 h. 
At 6 am and 6 pm, two hands form $\displaystyle { 180 }^{ o }$
Number of times they form $\displaystyle { 180 }^{ o }$ = 11 

Multiple choice maths measuring time time in 24 hour clock time difference time

A watch which gains uniformly was observed to be 5 minutes slow at 12 noon on a Sunday. On the subsequent Wednesday at 6:00 p.m., it was noticed that the watch was 5 minutes fast. When did the watch show the correct time?

  1. On Monday at 12 noon

  2. On Monday at 3:00 a.m,

  3. On Tuesday at 3:00 a.m.

  4. On Tuesday at 12 midnight

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

Since the watch is  5 minutes slow at 12 noon on a Sunday and 5 minutes fast on the subsequent Wednesday at 6:00 p.m, it will show the right time at a time exactly mid way of theses 2 times.
hours passed=24+24+24+6=78hrs
mid way will be 39hrs after Sunday noon, which will be 3:00 a.m. tuesdsay.

Multiple choice maths measuring time time in 24 hour clock time difference time

The minute and hour hands of a clock overlap every 60 minutes of correct time. How much does the clock lose or gain in a day?

  1. $130 \displaystyle \frac{10}{11}$ minutes
  2. $58 \displaystyle \frac{6}{7}$ minutes
  3. $143 \displaystyle \frac{5}{11}$ minutes
  4. $139 \displaystyle \frac{4}{11}$ minutes

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

In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.

To be together again, the minute hand must gain 60 minutes over the hour hand.

55 minutes are gained in 60 min.

60 min. are gained in [(60/55) * 60] min = $65\frac { 5 }{ 11 } $min.

Therefore, loss in 60 minutes =  $65\frac { 5 }{ 11 } -60=5\frac { 5 }{ 11 } $ min.

Loss in 24 hours = $5\frac { 5 }{ 11 } *\frac { 24*60 }{ 60 } $ = $130\frac { 10 }{ 11 } $min.

Therefore, the clock loses $130\frac { 10 }{ 11 } $ minutes in 24 hours.

Multiple choice maths measuring time time in 24 hour clock time difference time

A clock loses 5 seconds every hour. If the clock is set on Sunday at 12 noon, then what is the correct time the following Saturday, if the clock shows 12, midnight (give answer to the nearest minute)?

  1. II:53 p.m. on Saturday

  2. 11:47 p.m. on Saturday

  3. 00: 13 a.m. on Sunday

  4. 11: 52 p.m. on Saturday

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

Let the hours passed be $x$,
time shown on $clock 1=12:00 a.m$ saturday $(24*6+12hrs)$
$3600x-5x=156*60*60$,
$x=156.21hrs=156hrs$ and $13mins$
actual time $=12:13 a.m.$ saturday.

Multiple choice maths measuring time time in 24 hour clock time difference time

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes. How much in a day does the clock gain or lose?

  1. Gains $\displaystyle 56 \frac{8}{77}$ minutes
  2. Loses $\displaystyle 32 \frac{8}{11}$ minutes
  3. Loses $\displaystyle 9 \frac{10}{143}$ minutes
  4. Gains $\displaystyle 10 \frac{9}{143}$ minutes
  5. Gains $\displaystyle 10 \frac{10}{143}$ minutes
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.

To be together again, the minute hand must gain 60 minutes over the hour hand.

55 minutes are gained in 60 min.

60 min. are gained in [(60/55) * 60] min = $65\dfrac { 5 }{ 11 } $min.

But they are together after 65 min.

Therefore, gain in 65 minutes =  $65\dfrac { 5 }{ 11 } -60=\dfrac { 5 }{ 11 } $ min.

Gain in 24 hours = $\dfrac { 5 }{ 11 } * \dfrac { 24*60 }{ 65 } $ = 1440/143 min.

Therefore, the clock gains $(10 + 10/143 )$ minutes in $24$ hours.

Multiple choice maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

A clock is started at noon. By 10 min past 5, the hour hand has turned through

  1. $145^{o}$
  2. $150^{o}$
  3. $155^{o}$
  4. $160^{o}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Angle traced by hour hand in 12 h = $360^{o}$

Angle traced by hour hand in 5 h 10 min i.e., $\dfrac{31}{6} h$ $\implies (\dfrac{360}{12} \times \dfrac{31}{6})^{o}$ = $155^{o}$

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

A clock is set right at $8:00\ a.m$. The clock gains $10$ minutes in $24$ hours. What will be the right time when this clock indicates $1\ p.m$ on the following day?

  1. $11.40\ p.m$
  2. $12:00\ p.m$
  3. $10:00\ p.m$
  4. $12:48\ p.m$
  5. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The clock gains $10$ mins in $24$ hours,
It will gain 1 min in every $2.4$ hours.
Difference in time the clock indicates=$1$ p.m.-$8$ a.m. (the next day)
=$29$ hours,
Time gained=$\dfrac {29}{2.4}=12$ mins.
Actual time=$12:48$ p.m.

Multiple choice

How often do leap years occur?

  1. Every 4 years

  2. Every 5 years

  3. Every 6 years

  4. Every 7 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Leap years occur every four years, except for years that are divisible by 100 but not by 400.

Multiple choice

Two clocks are set correctly at 10 am on Friday. The first clock gains 2 minutes per hour and it gains twice as much as the second clock. What time will the second clock show when the correct time is 2 pm on the following Monday?

  1. 2:42 pm

  2. 3:16 pm

  3. 3:32 pm

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

First clock gains 2 min/hr. Second clock gains 1 min/hr. Time elapsed from Friday 10 am to Monday 2 pm is 72 + 4 = 76 hours. Second clock gains 76 minutes. 2 pm + 76 minutes = 3:16 pm.