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 physics heat and temperature anomalous expansion of water thermal expansion in solids, liquids and gases thermal expansion

A clock which keeps correct time at $20^{\small\circ}C$, is subjected to $40^{\small\circ}C$. If coefficient of linear expansion of the pendulum is $12\times10^{-6}$ per $^{\small\circ}C$. How much will it gain or loose in time?

  1. $10.3\space seconds/day$
  2. $20.6\space seconds/day$
  3. $5\space seconds/day$
  4. $20\space minutes/day$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\quad T = 2\pi\sqrt{\displaystyle\frac{l}{g}}$
$\quad \displaystyle\frac{\triangle T}{T} = 2\pi\times\displaystyle\frac{1}{2}(l/g)^{-1/2}\times\triangle l/l$
$\quad (\because T + \triangle T = 2\pi\sqrt{\displaystyle\frac{l+\triangle l}{g}})$
$\quad \therefore \displaystyle\frac{\triangle T}{T} = \displaystyle\frac{1}{2}\displaystyle\frac{\triangle l}{l} = \displaystyle\frac{1}{2}\propto\triangle\theta$
$\quad = \displaystyle\frac{1}{2}\times12\times10^{-6}\times(40-20) = 12\times10^{-5}$
$\quad \triangle T = T\times12\times10^{-5} = 24\times60\times60\times10^{-5} = 10.3\space s/day$

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

The hands of a clock coincide after every  $66$  minutes of correct time. How much is the clock fast or slow in  $24$  hours?

  1. $12 \frac { 108 } { 121 }$
  2. $11 \frac { 109 } { 121 }$
  3. $Both (A) \& (B)$

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

The angle between $2$ successive numbers in the clock is $\dfrac{360}{12}=30^{\circ}$

The angle between successive dots is $\dfrac{360}{60}=6^{\circ}$
For one rotation of minutes hand hours hand rotates by $30^{\circ}$
$\implies $ For increase in $1$ minute there is increase of $\dfrac{1}{2}^{\circ}$ for hours hand
Net decrease For $1$ min is $\dfrac{11}{2}^{\circ}$
For $x$ min the decrease must be $30^{\circ}$
$\implies x=\dfrac{60}{11}$
So the hands to co incide again it takes $60+\dfrac{60}{11}\implies 65\dfrac{5}{11}$ min
The clock shows $\dfrac{6}{11}$ min error for $66$ min

The clock shows $x$ min error for $24\times 60$ 
$\implies x=\dfrac{\dfrac{5}{11}\times24\times60}{11}=11\dfrac{109}{121} $

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

Choose the most appropriate option.
The angles between the hands of a clock when the time is $4:25$ am is?

  1. $14.5$ degrees
  2. $12.5$ degrees
  3. $17.5$ degrees
  4. $13.5$ degrees
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The hour hand rotates $0.5^o$ per minute while the minute hand rotates $6^o$ per minute.

At exactly four, the hour hand as completed $240$ minutes $= 120^o$. 

Hence angle between minute and hour hand at that point is $120^o$.

At $4:25,$ the minute hand has moved $25\times 6= 150^o.$

Thus angle between minute hand and $12$(on the clock) is $150^o.$

But at the same time, even the our hand has moved $0.5\times 25= 12.5^o.$

Now, the angle between the hour hand and $12$(on the clock) is $120+12.5=132.5^o$.

Now the angle between the two hands of the clock $=150^o-132.5^o$ 
                                                                                       $ = 17.5^o.$
                                                                       
Multiple choice maths measuring time time in 24 hour clock time difference time

A clock, which loses 5 minutes per day, is set to show the correct time at 12 noon on a Sunday. What time does the clock show at 12 noon on the next Sunday?

  1. 11 a.m.

  2. 12 noon

  3. 11.35 a.m.

  4. 11.25 a.m.

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

The clock loses $5$ minutes per day
in 7 days, time lost $=5 \times 7=35mins$
actual time $=12'o clock$,
time shown $=11:25 a.m.$

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

A clock is set to show the correct time at 11:00 a.m. The clock gains 12 minutes in 12 hours. What will be the correct time when the clock indicates 5:30 p.m. the next day?

  1. 5.00 p.m.

  2. 5.10 p.m.

  3. 5.20 p.m.

  4. 6.00 p.m.

  5. 5.48 a.m.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The clock gains 12 mins in 12 hours,
It will gain 1 min in every 1 hour.
Difference in time the clock indicates=5:30 p.m.-11 a.m. (the next day)
=30.5 hours,
Time gained=30.5/1=30 mins.
Actual time=5 p.m.

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. One clock is losing 2 minutes per hour and the other clock is gaining 3 minutes per hour. If the clock which is losing 2 minutes per hour shows 3:00 p.m. the next day, what time does the clock gaining 3 minutes per hour show?

  1. 5.30 p.m.

  2. 4.00 p.m.

  3. 4.15 p.m.

  4. 5.00 p.m.

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

In each hour, the time difference between the 2 clocks will increase by 5mins
time passed $=24+2+3=29hrs$ on clock 1
Real time on clock $1=4 p.m$
difference between 2 clocks=$5*30=150mins$,
time on clock $2=3hrs+2hrs+30mins$
$=5.30 p.m$

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

At what time, between twelve o'clock and one o'clock, will the hands of the clock overlap again?

  1. 12 hours $\displaystyle 50 \frac{2}{11}$ minutes

  2. 12 hours 45 minutes

  3. 12 hours 59 minutes

  4. Never happen

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

At twelve o'clock, the 2 hands are overlapping. 
As the minutes pass, the minutes hand moves farther away from the hours hand.
Therefore, between twelve o'clock and 1 o'clock, the hands will not overlap again.

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

A watch showed five past five on Wednesday evening when the correct time was 5:00 p.m. It loses uniformly, and was 5 minutes slow after two days at 7:00 p.m. When did the watch show the correct time?

  1. Thursday 6:00 a.m.

  2. Thursday 6:00 p.m.

  3. Thursday 6:30 p.m.

  4. Thursday 5:00 a.m.

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

Since the watch was 5 minutes fast on Wednesday evening, 5:00 p.m. and was 5 minutes slow after two days at 7:00 p.m., the correct time would be at the mid point of these 2 times.
Time difference=(24+24+2)50 hours,
So the right time will be 25 hours past 5 p.m. Wednesday,
I.e, 6 p.m. on Tuesday.

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

A clock gains 10 minutes in 2 hours. It is set right at 10:I0 a.m. When the clock shows 4:40 p.m. on the same day, what is the correct time?

  1. 4.54 p.m.

  2. 5.00 p.m.

  3. 5.10 p.m.

  4. 4.10 p.m.

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

Let the hours passed be x,
time difference as per clock=5hrs and 30mins 
actual time=x*60+x*5=330,
x=5 hrs,
actual time=4:10

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

A  certain $12$-hour digital clock displays the hour and minute of a day. Due to a defect in the clock whenever the digit $1$ is supposed to be displayed it displays $7$. What fraction of the day will the clock show the correct time?

  1. $\displaystyle \frac {1} {2} $
  2. $\displaystyle \frac {5} {8} $
  3. $\displaystyle \frac {3} {4} $
  4. $\displaystyle \frac {5} {6} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The clock will show 1 in an hour for 19 time for 11 hours it will show the incorrect time for $(19 \times 11)$ time. The last 12th hour will always show the in correct time so total in correct time.

$(19 \times 11 + 60)$ min = $269$ min

there are $24$ hours in a day to $ = 269 \times 2 = 538 $ min

$538$ min = $\displaystyle \frac {269} {30} = 9 $ hours

the fraction day when the clock shows the correct time is $\displaystyle = 1 - \frac {9} {24} $

                                                                                                 $\displaystyle = 1 - \frac {3} {8} = \frac {5} {8}$

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

There are two clocks, both set to show correct time at 9:00 a.m. One clock loses 1 minute every hour, and the other gains 1 minute every hour. By how many minutes do they differ at 10:00 p.m. on the same day?

  1. 24 minutes

  2. 30 minutes

  3. 28 minutes

  4. 26 minutes

  5. 13 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

After each hour, the difference between clocks will increase by 2 minutes.
At 10 p.m., hours passed=13,
Difference=13*2=26 minutes.

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

Imagine a clock where the hour hand makes only one revolution in 1 day (i.e., 24 hours) whereas the minute hand completes one revolution in 1 hour. What is the angle between the two hands at 14:50 hours as per this clock?

  1. 90$^o$
  2. 120$^o$
  3. 77.5$^o$
  4. 162.5$^o$

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

14:50 in the current clock would be indicated by the hour hand a little before midway of 7 and 8 and minute hand would be on 10.

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

How many times do the hands of a clock make an angle of 90$^o$ in 36 hours?

  1. 11

  2. 22

  3. 44

  4. 72

  5. 66
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

If you switch to a rotating coordinate system in which the hour hand stands still, then the minute hand makes only 11 revolutions, and so it is at right angles with the hour hand 22 times. In 36 hours, you get 322=66.