# Clock logical Reasoning solved problems

In this post we will discuss logical reasoning questions related to clocks. Clock is one of the important chapter of verbal ability syllabus and lot of questions are frequently asked in the competition exams.

In order to solve questions fast, try to draw picture in your mind how clock needles move
1. Minute hand travels 360 degree in 60 minutes
==> So, Minute hand moves 6 degree in 1 minute

2. Hour hand moves 360 degree in 12 hours
==> So, Hour hand moves 30 degree in 1 hour
==> Also, Hour hand moves 0.5 degree in 1 minute

Try to remember the above points, it will help you solve questions faster.

## Clock Questions Verbal Ability

(Q.1) The minute hand of clock overtakes the hour hand at intervals of 64 minute of correct time. How much a day clock gain or lose ?

(a) 360/11 minutes
(b) 360/12 minutes
(c) 360/13 minutes
(d) 360/14 minutes

Remember that in ideal watch, the minute hand overtakes hour hand in 65\frac { 5 }{ 11 } minutes

But in this watch minute hand overtakes hour hand in 64 minutes
This means that the watch is moving fast

We can calculate how fast the watch is moving by following calculation
==> Ideal Watch Time – Watch Time
==> 65(5/11) – 64
==> \frac { 16 }{ 11 }

Hence for every 64 minutes, the clock is moving 16/11 minute fast

==> In 64 minutes clock gains => 16/11 minutes
==> In 1 minute clock gain=> 16/11 * 1/64
==> In 1 day clock gains => 16/11 * 1/64 * 60 *24 minutes ==> 360/11 minutes

Hence in 1 day, the clock gains 360/11 minutes
option (a) is the right answer

(Q.2) A clock is set right at 8 a.m. on Sunday. It gains 8 mins in 24 hours. What is the correct time when the clock indicates 9 p.m. on upcoming Sunday ?

(a) 9 PM
(b) 8 PM
(c) 11 PM
(d) 7 PM

Total hours from Sunday  8 a.m. to next Sunday 9 PM = 181 hours

According to question the clock gains 8 min. in 24 hours
==>24 hours ideal time => clock gained 8 mins
==> 24 hours ideal time ==> 24 hours + 8 mins (clock time)
==> 24 hours + 8/60 hrs
==> 362/15 hours

Hence in 24 hours, the clock covers 362/15 hours
So, in 1 hour, the clock gained ==> \frac { 362 }{ 15 \quad \times \quad 24 }

Now in 181 hours, the clock covers ==>
==> 182 hours

So in this time period, our clock is fast by = 182-181 = 1 hours

From the above calculation we can see that in the given time period, the clock is fast by 1 hour
so on next Sunday, if the clock is showing 9 PM, it means that the actual time is ==> 9 – 1 => 8 PM

So, 8 PM is the real time
option (b) is the right answer

Q.3 A clock is set right at 10 a.m. on Sunday it loses 8 mins. In 24 hours. What is the correct time when the clock indicates 9 p.m. on next Sunday ?

(a) 9 PM
(b) 8 PM
(c) 11 PM
(d) 10 PM

Total hours of clock from 10 a.m. Sunday to 9 p.m. on following Sunday = 179 hours

According to question , the looses 8 min in 24 hours

In 24 hours ideal time, the clock covers
=> 24 hours – 8 min. = 23 hours 52 min.
==> 23 + 52/60
==> 345 + 13 / 15
=> 358/15 hours of given clock
Hence in 24 hours, the clock covers = 358/15 hours

358/15 hours of given clock = 24 hours of correct clock

1 hour of given clock =  24 X 15/358 hours of correct clock

179 hours of given clock = 24X15X179 / 358 = 180 hours of correct clock

It means 1 hour more

Correct time = 9 p.m. + 1 hour = 10 p.m.
Option (d) is the right answer

(Q.4) A watch which gains uniformly is 4 min. slow at 9 a.m. on Sunday, and is 4 min 15 sec. fast at 9 p.m. on upcoming Friday. When was it correct ?

(a) 1:00 AM
(b) 4:00 AM
(c) 5:00 AM
(d) 2:00 AM

Time period is between Sunday 9 a.m. and upcoming Friday 9 p.m. (total 132 hours)

Total watch gains 4 min + 4 min 15 sec => 8 min 15 sec
Converting into minutes
==> 8 + 15/60 = 8 + ¼ = 33/4 min.

Hence in 132 hours the clock gained 33/4 minutes
Total hours = 132 hours

33/4 min gain in 132 hours
1 minute gain in = 132 X 4 / 33 hours

As the clock was slow 4 minutes, total time taken to get into right time
4 minute gain in==> 132 X 4 X 4 / 33 ==> 64 hours

Hence in 64 hours, the clock will gain 4 minute and get into right time
9 a.m. Sunday + 64 hours = 9 a.m. Sunday + 2 days 16 hours = 1 a.m. Wednesday

In 1:00 AM Wednesday, the clock will show right time.
option (a) is the right answer

(05) After 9’0 clock at what time between 9 p.m and 10 p.m will the hour and minute hands of a clock point in opposite direction?

(a)15 minutes past 9
(b)16 minutes past 9
(c) 16 \frac{4}{11} minutes\ past\ 9
(d) 17 \frac{4}{11} minutes\ past\ 9 \\ \\ Read Solution

Using the Formula
\theta =30H-\frac{11}{2} M

Where
H = Hour Hand
M = Minute Hand
\theta = Angle between Minute hand and Hour hand

Now H=9
\theta =180\degree \ (since\ hands\ are\ in\ opposite\ direction) \\\ \\ ⟹ 180=30\times 9-\frac{11}{2} \times M \\ \\ ⟹ 180=\frac{540-11M}{2} \\ \\ ⟹ 360=540-11M \\ \\ ⟹ 11M=180 \\ \\ ⟹ M=\frac{180}{11} =16.36\ min \\ \\ ⟹ 16\frac{4}{11} \ minutes\ past\ 9

option (c) is the right answer

(06) At what time are the hand of clock together between 6 and 7?

(a) 32\frac{8}{11} \ minutes\ past\ 6 \\\ \\ (b) 34\frac{8}{11} \ minutes\ past\ 6 \\\ \\ (c) 30\frac{8}{11} \ minutes\ past\ 6 \\\ \\ (d) 32\frac{5}{7} \ minutes\ past\ 6 \\ \\ Read Solution

To overlap the minute hand has to gain 30 minutes.

We know that:
In 60 minutes, Minute hand cover 360 degrees,
In 60 minutes, Hour hand cover 30 degrees,

Hence in every 60 min. minute hand cover 330 degrees more than the hour hand

Also, 330 degrees = 55 min. in clock
So, in every 60 min. minute hand is 55 min. ahead of hour hand

Now, 30 minutes will be gained in =\frac{60}{55} \times 30 \\\ \\ =\frac{36}{11} \ = \ 32\frac{8}{11} \ minutes

So the hands will overlap e 32\frac{8}{11} minutes past 6

Option (a) is the right answer

(07) A clock goes fast by one minute during the first hour, by two minutes at the end of second hour, by 4 minutes at the end of 3rd hour, by 8 minutes by the end of 4th hour, and so on. At the emd of which hour, will it be fast by just over sixty minutes?
a)  fifth
b) sixth
c) seventh
d) eighth

First hour ⟹ 1 min
Second hour ⟹ 2 min
Third hour ⟹ 4 min
Fourth hour ⟹ 8 min
Fifth hour ⟹ 16 min
Sixth hour⟹ 32 min
Seventh hour ⟹ 64 min
Hence at the end of 7th hour it will be fast by just over 60min
Option (c) is the right answer

(08) A clock goes slow from midnight by 5 min. at the end of the 1st hour, by 10 min. at the end of the 2nd hour, by 15 min. at the end of the 3rd hour and so on. What will be the time by this clock after 6 hours?

a) 6:00am
b) 5:30am
c) 6:30am
d) 5:15am

Clock is getting slow by 5 min per hour from midnight,
So, after 6 hours clock will go slow by = 6* 5= 30 min.
Time shown by the clock = 6:00 – 0:30= 5:30 am
Option (b) is the right answer

(09) A clock only with dots marking 3,6,9 and 12 0′ clock positions has been kept upside down in front of mirror. A person reads the time in the reflection of the clock as 12:30. What is the actual time?

(a) 12 O’ clock
(b) 12:30
(c) 6 O’ clock
(d) 03:45

For actual Time we have to subtract 12:30 from 17:90, because both hands of clock are between 6 to 12.

17:90-12:30=5:60=6:00

Concept: If hour hand lies between 6 to 12 and minute hand is lies between 6 to 12 then we have to subtract time from 17:90 to get actual time.

Option (c) is the right answer

(10) A clock only with dots marking 3,6,9 and 12 0′ clock positions has been kept upside down in front of mirror. A person reads the time in the reflection of the clock as 9.50. What is the actual time?

(a) 2:15
(b) 8:40
(c) 8:50
(d) 4:15