Tag: time in 24 hour clock

Questions Related to time in 24 hour clock

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:

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

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

maths measuring time time in 24 hour clock time difference time

  1. $2$

  2. $11$

  3. $13$

  4. $14$

Show answer
Correct Option: B
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 

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?

maths measuring time time in 24 hour clock time difference 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

Show answer
Correct Option: C
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.

A clock is set to show the correct time at 12:00 noon. Immediately, due to some mechanical defect, both the minute hand and the hour hand started moving in the reverse direction (anticlockwise direction). What is the correct time when this clock shows 8:25?

maths measuring time time in 24 hour clock time difference time

  1. $4:25$

  2. $3:25$

  3. $7:25$

  4. $7:35$

  5. $3:35$

Show answer
Correct Option: E
Explanation:

When the hands are moving anticlockwise, we can assume that the time shown is the mirror image of actual time.
Assume that there is a line drawn between 12 and 6 on the clock, this can be a line of symmetry.
When we take the mirror image of this clock, the hands that are on the right side of this line will appear equidistant on the left side of the line and vice versa.
The time indicated is 8:25, the hour mid way after 8 and the minute hand on 5.
Its mirror image will become, the hour mid way before 4 and the minute hand on 7, i.e, 3:35.

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?

maths measuring time time in 24 hour clock time difference time

  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

Show answer
Correct Option: A
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.

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)?

maths measuring time time in 24 hour clock time difference time

  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

Show answer
Correct Option: C
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.

Write the following $24$ hr clock into $12$ hour clock.
$23:42$ .

maths measuring time time in 24 hour clock time difference time

  1. $9:42\ am$

  2. $11:42\ pm$

  3. $11:42\ am$

  4. $9:42\ pm$

Show answer
Correct Option: B
Explanation:
$23:42$
Since hour is more than $12$ it is p.m.
$23-12=11$
Time is $11:42\ pm$

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?

maths measuring time time in 24 hour clock time difference time

  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

Show answer
Correct Option: E
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.