# 17. Quantitative Aptitude Questions - CLOCKS Solved Problems

**Clocks**

**Aptitude Questions Clocks - Solved Problem 1**

What is the angle made
by minute angle in 16 minutes?

a) 8

^{0}b)32^{0}c)96^{0 }d) 48^{0 }e)90^{0}
Answer: C

Explanation:

The angle made by minute
hand in 1 minute is 6

^{0.}
In 16 minutes, the angle
made by 16 minutes is

= 16 x 6

= 16 x 6

^{0 }=96^{0}

**Aptitude Questions with Answers Clocks - Solved Problem 2**

2. What is the angle
made by hour hand in 30 minutes?

a) 5

^{0}b)10^{0}c)180^{0}d) 15^{0 }e)28^{0}
Answer : D

Explanation:

The angle made by minute hand in 1 minute is
(1/2)

^{0}.
In 16 minutes, the angle made by 30 minutes is = 30 x
½ =15

^{0}**Quantitative Aptitude Problems with Answers Clocks - Solved Problem 3**

3. What is the
difference between angles made by minute hand and hour hand in 24 minutes?

a) 185

^{0}b)120^{0}c)180^{0}d) 132^{0 }e)208^{0}
Answer: D

Explanation : The angle
made by minute hand in 24 minutes = 24 x 6

^{0}=144^{0}
The angle made by hour hand
in 24 minutes =24 x

1
2

=12^{0}
The difference is =
144 -12 =132

^{0}**Arithmetic Aptitude Questions with Solutions Clocks - Solved Problem 4**

4.How often the hands of
clock at right angle everyday ?

a)11 times b)22 times c)44 times d)55
times e)66 times

Answer : C

Explanation:

In every hour there are
two positions in which the minute hand and hour hand are at right angle. Each
of these positions is repeated 22 times in every 12 hours.

Therefore in a day ( 24 hours ), the two hands are perpendicular to each other

22 + 22 =44 times.

**Aptitude Clocks - Solved Problem 5**

5. How many times the hands of a clock are in a straight line every day?

a)
11 times b)22 times c)33 times d)44 times e)55 times

Answer : D

Explanation: As we know,
any relative position of the two hands of a clock is repeated 11 times in every
12 hours.

In every 12 hours ,
two hands coincide ( when the two hands coincide, they are always on same
straight line ) 11 times and two hands are opposite to each other (but
in same straight line )11 times .

∴ in every 12 hours , two hands are in straight line
11 +11 =22 times.

∴ in every 24 hours , two hands are in straight line
44 times.

**Aptitude Clocks - Solved Problem 6**

**6. A clock strikes 5 takes 16 seconds. In order to strike 10 at the same rate, the time taken is**

a) 24 seconds b)30
seconds c)36 seconds
d)32 seconds e)40 seconds Answer : C

Explanation :

There are 4 intervals when
the clock strikes 5.

Time taken in 4 intervals
= 16 seconds

∴ Time taken for
1 interval = 4 seconds

In order to strike
10, there are 9 intervals. For which the time taken is 9 x 4 =36 seconds

**Aptitude Clocks - Solved Problem 7**

**7. What is the angle between the minute hand and hour hand at 20 minutes past 4 O' clock ?**

a)
5

^{0}b)10^{0}c)180^{0}d) 15^{0}e)20^{0}**Answer : B**

**Explanation :**To find the angle between hour hand and minutes at H hours M minutes , θ =( 30 X H) - ( (

11
2

) M)
= (30 X 4) - ((

11
2

) x
20)
= 120 - 110
= 10

^{0}**Aptitude Clocks - Solved Problem 8**

8.At what time between 4 and 5’O
clock are the two hands of the clock coincide ?

a)4.21

9
11

b)4.20 c)4.23
7
11

d)4.22 e)4.19
9
11

^{ }**Answer : A****Explanation :**At 4'O clock , the hour hand is at 4 and the minute hand is at 12. Hence minute hand is 20 minutes spaces behind the hour hand.

The two hands will coincide
each other , when the minute hand gains 20 minutes spaces over the hour hand.

We know that, the minute hand
gains 55 minute spaces in 60 minutes.

To gain 1 minute space , it will
take

60
55

minutes.
To gain 20 minutes spaces , it
will take 20 x

60
55

= 20 x
12
11

=21
9
11

minutes
∴ The two hands coincide at 21

9
11

minutes past 4.**Aptitude Clocks - Solved Problem 9**

9. Find the time between 8 and 9’O Clock when the two hands of a clock are
in the same straight line.

a) 8.41

9
11

b)8.43
7
11

c)8.47
3
11

d)8.44
3
11

e)None the above**Answer:**

**B**

**Explanation :**

Two hands of a clock are in the
same straight line in two cases:

**Case 1:**When the two hands are in exactly opposite direction.

This equals 180

^{o}=180^{o}/6=30 minute spaces apart.
At 8’O Clock, the minute hand is
(8×5)=40 minute spaces behind the hour hand. Therefore, the minute hand will
have to gain (40-30)=10 minute spaces over the hour hand.

Q Gain of 55 minute spaces equals 60
minutes.

Q Gain of 40 minute spaces

60
55

×
10=
120
11

=10
10
11

minutes.
Q The minute hand will be is exactly
opposite direction to the hour hand at 10

10
11

minutes past 8’O Clock.**Case 2:**When the two hands coincide i.e, 0 minute spaces apart.

In this case the minute hand will have to gain (8×5)=40 minute spaces over the
hour hand.

To gain 40 minute spaces=

60
55

×40=
480
11

= 43
7
11

times
Q The two hands will hands will coincide
at 43

7
11

minutes past 8 ‘O Clock.**Aptitude Clocks - Solved Problem 10**

10. At what time between 5 and 6’O clock will the two hands of a clock be at
right angle?

a) 5.43

7
11

b)5.10
10
11

c)5.12
8
11

d)5.13
8
11

e) 5.09
7
11

**Answer : Both A and B**

**Explanation:**At 5’O Clock the minute hand is (5×5)=25 minute spaces behind the hour hand.

The two hands will be at a right
angle when either (i) the minute hand is 15 minute-spaces behind the hour hand
or (ii) the minute hands are 15 minute-spaces ahead of the hour hand.

**Case1:**When the minute hand 15 minute-spaces behind the hour hand.

For the two hands to be in this
position, the minute hand must gain (25-15) =10 minute-spaces over the hour
hand.

Q 55 minute spaces are gained in 60
minutes.

Q 10 minute-spaces are gained in

60
55

×10=
120
11

=10
10
11

minutes.
Q The two hands will be at right angle
at 10

10
11

minute past 5’O clock.**Case 2:**when the minute hand 15 minute-spaces ahead of the hour hand.

To be in this position, the minute hand must gain (25+15)=40 minute spaces.

Q 40
minute-spaces are gained in

60
55

×40 =
480
11

=43
7
11

times.
Q The two hands will be at right angle
at 43

7
11

minutes past 5’O Clock.**Aptitude Clocks - Solved Problem 11**

11. At what time between 4 and 5 are the hands 2 minutes spaces apart?

a) 4 19

7
11

and 4.22
b)4.21

7
11

and 4.24
c) 4. 19

7
11

and 4.24
d) 4.18

9
11

and 4.24
2
11

e) None of the above

**Answer : C**

**Explanation:**4’O Clock, the two hands are 20 minute spaces apart.

**Case 1:**When the minute hand is 2 minute spaces behind the hour hand.

In this, the minute hand
will have to gain (20-2) i.e 18 minute spaces. Now, we know that 18 minute
spaces will be gained in 18 ×

12
11

=
216
11

=19
7
11

minute.
Q The two hands will be 2 minutes apart
at 19

7
11

minutes past 4.**Case 2:**when the minute hand is 2 minute spaces ahead of the hour hand.

**In this case, the minute hand will have to gain (20+2) i.e., 22 minute spaces.**

Now the 22 minute spaces will be gained in

22×

12
11

= 24 minutes
The
hands will be apart at 24 minute past 4

**Aptitude Clocks - Solved Problem 12**

When do the two hands of
a clock of just after 3 pm make 30 º angles between them?

a)3:15:00 b)3:10:54 c)3:01:59 d) 3:20:21 e)3:18:00

a)3:15:00 b)3:10:54 c)3:01:59 d) 3:20:21 e)3:18:00

**Answer:(B)**

**Explanation:**To find the angle between hour hand and minutes at H hours M minutes,

θ =30H –

11
2

M
Here the angle given
is 30=> - 30 = 30 x 3 –

11
2

M ( We take + and – angles , because minute
hand 30^{0}behind the hour hand and 30^{0}aheadof the hour hand)
11
2

M = 60 => M=
120
11

= 10
10
11

minute
= 10 min 54s

(We have the answer in the given
choices , we need not compute the another time with +30

^{0})
∴Required time = 3:10:54

**Aptitude Clocks - Solved Problem 13**

A clock strikes ones at
1 O’clock, twice at 2 O’clock and so on. What is the total number of striking
in a day

a) 12 b) 156 c) 78 d) 24 e) 48

a) 12 b) 156 c) 78 d) 24 e) 48

**Answer:(B)**

**Explanation:**The clock strickes once at 1 O’clock, twice at 2 O’clock, thrice at 3 O’clock and so on.

So in 12 hours , the total number of
strikes = 1 + 2 + 3 + 4 + ---- + 12

(Sum of the first n natural numbers=

n(n+1)
2

)
=

12(12+1)
2

=78
In 12 hours, the total strikes are 78.

∴ In a day (24
hours) , total no. of strikes = 2 x 78 = 156

**Aptitude Clocks - Solved Problem 14**

Three cuckoo clocks are
such that the cuckoos chime after every 9 minutes, 15 minutes and 35 minutes
respectively. If the 3 clocks chime simultaneously at 3 p.m, what time will
they chime together again?

a)8 :15 p.m b)9:15 p.m c)10.30 p.m d) 11.00 p.m e)00.45 p .m

**Answer:B**

**Explanation:**

Three cuckoo clocks are such that the
cuckoos chime after every 9 minutes, 15 minutes and 35 minutes respectively.

All the three clock chime
simultaneously at 3 p.m

They will again chime together =>
LCM of 9 minutes, 15 minutes and 35 minutes

ð 315 minutes

After 135 minutes , 3 clock will chime
together

The time at they will chime again together = 3
p.m + 315 minutes

= 8:15 p.m

**Aptitude Clocks - Solved Problem 15**

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

a)
11

11
143

minutes b)10
10
143

minutes c)12
11
143

minutes
d)
9

11
143

minutes e)
13
11
143

minutes**Answer: B**

**Explanation:**

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

To coincide each
other again, the minute hand must gain 60 minutes over the hour hand.

Now, 55 min. are
gained in 60 min.

∴ 60 min. are gained in

60
55

x 60 min. = 65
5
11

min.
But, in the given problem, the minute hand overtakes the hour hand at
intervals of 65 minutes.

In the given
clock, the two hands meet at 65 minutes instead of 65

5
11

min.
Gain in every 65
minutes. =65

5
11

-65 min. =
5
11

min.
The clock in question gains

5
11

minutes
in 65 min.
The clock gains in a day (24 hours) =

5
11

X
1
65

X 24 X 60 =
1440
143

minutes = 10
10
143

**Aptitude Clocks - Solved Problem 16**.

There are two clocks A
and B. The hands of the clock A moves normally as clockwise while in clock B
(due to reverse connection) they move anticlockwise. Initially the two hands of
both clocks are at mark showing 12. If after some time, the angle between the
directions of two hour hands is 90º (for the first time), then at the same instant
the angle between the directions of minute hand will be

a)0

^{0}b) 60º c) 120º d)180º e) 90^{0}**Answer:**

**A**

**Explanation:**The angle between the two hour hands after some time is 90

^{0}.

As the both started at 12 ‘o clock,
the hour hand of clock A makes 45

^{0}and the hour hand of clock B makes 45^{0}from their initial position.
The hour hand of
clock A moved 45º from its initial position. Therefore, number of minutes the
hour hand makes is 45 x 2 = 90 minutes

In 90 minutes, the minute hand makes
angle of 90 x 6

^{0}= 540^{0}
As 360

^{0}is a complete revolution = > 540^{0}= 360^{0}+ 180º from its initial position.
As both hands move 180

^{0 }in either direction, the minute hands of two clocks coincide, i.e. the angle between them is zero degree.**Aptitude Clocks - Solved Problem 17**

A watch was set correct
at 12’O clock. It loses 10 minutes per
hour. What will be the angle between the two hands of the clock after 1 hour?

a) 75º b) 85º c) 90º d) 105º e)120

a) 75º b) 85º c) 90º d) 105º e)120

^{0}**Answer:(B)**

**Explanation:**

**The clock loses 10 minutes per hour**

SO the clock shows only 50 minutes for 60
minutes.

After 1 hour, the
watch show the time 12 : 50

The angle between
the two hands of the clock after 1 hour i.e 60 minutes (i.e. 50 minutes
according to the clock) = 30H –

11
2

M
=(30 x 12) –

11
2

x 50=360º – 275º = 85º**Aptitude Clocks - Solved Problem 18**

A clock is set right at
7:10 am on Thursday, which gains 12 minutes in a day. On Sunday if this watch
is showing 3: 50 pm. What is the correct time?

a)2:50 pm b) 3:10 pm c) 3:30 pm d)4:30 pm e) 4.10 p.m

a)2:50 pm b) 3:10 pm c) 3:30 pm d)4:30 pm e) 4.10 p.m

**Answer: B**

**Explanation:**Total number of hours from Thursday 7.10 a.m. to the 3 : 50 p.m . on Sunday.

=>24 x 3 + 8 hours 40 minutes = 80
hours 40 minutes. (80 4

40
60

=
242
3

hours)
The clock gains
12 minutes in every 24 hours.

24 hours 12 min.
of this clock =24 hours of correct clock,

i.e.121/5 hours of this clock = 24 hours of
correct clock

∴ 80 hours 40 minutes of this clock =24
X

5
121

X
242
3

) hours of correct
clock
= 80 hours of correct clock

Therefore the correct time is 7:10 a.m + 80 hours = 3:10 p.m.

**Aptitude Clocks - Solved Problem 19**

A clock is set right at
Tuesday 10 a.m . The clock gains 10 min in 24 hours What will be the correct
time on the following Thursday, when the watch indicates 8 p.m.?

a) 8.36 p.m. b) 8.40 p.m. c)7.36 p.m. d) 7.52 p.m e)8.12 p.m

a) 8.36 p.m. b) 8.40 p.m. c)7.36 p.m. d) 7.52 p.m e)8.12 p.m

**Answer: A**

**Explanation:**

Total number of
hours from Tuesday at 10 a.m. to the following Thursday at 8 p.m.

ð 24 x 2 + 10 = 58
hours

24 hours 10 minutes of this clock = 24 hours of a correct clock.

145
6

Hours of the incorrect clock = 24
hours of correct clock.
58 hours of the incorrect clock =

(24 x 6)
145

X 58 hours of correct clock
= 57

3
5

hours of correct clock.
Thus, the correct time on the following
Wednesday will be 8.36 p.m.

**Aptitude Clocks - Solved Problem 20**

A clock was correct at 2
p.m, but then it began to lose 30 minutes each hour. It now shows 6 pm, but it
stopped 3 hours ago. What is the correct time now?

( a) 8.30
pm. B)12 midnight c)11 p.m. d)1.30
a.m. e)1 a.m

**Answer: E**

**Explanation :**The clock loses 30 minutes per hour. And the clock set correct at 12 noon.

30 minutes of this clock = 60
minutes of the correct clock

From 2 p.m to 6 p.m , total number of
hours = 4 hours

4 hours of this clock => 4 x
60/30= 8 hours

The correct time when the clock
show 6 p.m = 6 p.m + 4 = 10 p.m

The clock stopped 3 hours ago , So
present time is 10 p.m + 3 hours = 1 a.m