Tag: time

Questions Related to 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?

maths measuring time time in 24 hour clock time difference time

  1. $\displaystyle \frac {1} {2} $

  2. $\displaystyle \frac {5} {8} $

  3. $\displaystyle \frac {3} {4} $

  4. $\displaystyle \frac {5} {6} $

Show answer
Correct Option: B
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} $

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

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?

maths measuring time time in 24 hour clock time difference time

  1. 24 minutes

  2. 30 minutes

  3. 28 minutes

  4. 26 minutes

  5. 13 minutes

Show answer
Correct Option: D
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.

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?

maths measuring time time in 24 hour clock time difference time

  1. 90$^o$

  2. 120$^o$

  3. 77.5$^o$

  4. 162.5$^o$

  5. None

Show answer
Correct Option: C
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.

A clock strikes once at one o'clock, twice at two o'clock, thrice at three o'clock, and so on. How many times, in total, will it strike in 24 hours?

maths measuring time time in 24 hour clock time difference time

  1. 144

  2. 288

  3. 300

  4. 156

  5. 72

Show answer
Correct Option: D
Explanation:

Clock strikes the same number of times as the hour that it is in, i.e, once at 1. 
The hours on the clock range from 1 to 12.
In a span of 24 hours, it will complete the cycle twice.
number of times it strikes=2(1+2+...12)
=156

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

maths measuring time time in 24 hour clock time difference time

  1. 11

  2. 22

  3. 44

  4. 72

  5. 66

Show answer
Correct Option: E
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.

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

maths measuring time time in 24 hour clock time difference time

  1. 6

  2. 1/10

  3. 12/5

  4. 5/12

  5. None of these

Show answer
Correct Option: D
Explanation:

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

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

maths measuring time time in 24 hour clock time difference time

  1. $\displaystyle 100^{\circ}$

  2. $\displaystyle 107^{\circ}$

  3. $\displaystyle 106^{\circ}$

  4. $\displaystyle 108^{\circ}$

Show answer
Correct Option: D
Explanation:

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

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

maths measuring time time in 24 hour clock time difference time

  1. $7\displaystyle\frac{1}{2}$

  2. $11\displaystyle\frac{1}{2}$

  3. $15$

  4. $23$

Show answer
Correct Option: C
Explanation:

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

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?

maths measuring time time in 24 hour clock time difference time

  1. 8:30 p.m.

  2. 9:00 p.m.

  3. 8:45 p.m.

  4. 9:30 p.m.

  5. None of these

Show answer
Correct Option: B
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.

A clock has numbers $1$ to $12$. If a clock has a shape of a circle, then the degree measure made by an arc between any two consecutive numbers of the clock is

maths measuring time time in 24 hour clock time difference time

  1. $60$

  2. $30$

  3. $45$

  4. $90$

Show answer
Correct Option: B
Explanation:

$12\rightarrow \frac { 360 }{ 12 } 30$