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** **__Wipro Placement Papers - Model Problems on Clocks __

__Wipro Placement Papers - Model Problems on Clocks__##
__Wipro Placement Papers with Solutions –Problems on
Clocks____ 1__
In a conventional clock, how many times does the minute hand pass the hour hand between noon and midnight?
a) 10 times b)11 times c)12
times d)15 times
Answer : A
Explanation :
In 12 hours, the hour hand goes around the
dial just once and the minute hand goes around 12 times.
Therefore they pass each other (12 – 1) = 11
times.
One of these 11 times is 12 midnight also.
But between noon and midnight is asked.
So we don’t count either noon or midnight
Therefore the answer is 10.

__Wipro Placement Questions with Answers –
Problems on Clocks 2__
How many times in a
day, the hands of a clock are straight?

a) 22 b)
24 c) 44 d) 48

Answer : C
Explanation: Any relative
position of the two hands of a clock is repeated 11 times every 12 hours.
In every 12 hours,
two hands coincide (when the two hands coincide, they are always on the same
straight line ) 11 times and two hands are opposite to each other (but
in the same straight line )11 times.
∴ In every 12 hours, two hands are in a straight line
11 +11 =22 times.
∴ In every 24 hours,
two hands are in a straight line 44 times.

__Wipro Placement Papers with Answers – Clocks Solved Problem 3__
How many times do the hands of a
clock point towards each other in a day?
a)12 b)
18 c) 22 d)
24
Answer : C
Explanation :
In one hour, the two hands point
towards each other only once.
The hands of a
clock point towards each other 11 times in 12 hours. (Because between 5 O.’
clock and 7 O’ clock, at 6 O’clock only
they point towards each other)
In 12 hours, it happens 11 times.
Hence in a day ( 24 hours), 22 times.
So, in a day the two hands point
towards each other 22 times

__Wipro Placement Questions with
Solutions – Model Problems on Clocks 4__
At 3.40, the hour
hand and the minute hand of a clock form an angle of

a) 120° b)
125° c) 130° d) 135°

Answer: C

Explanation :

The direct
formula to find the angle between two hands when the time in the clock is
H: M
Angle = |30H -$\frac{11}{2}$
M|
Here the given
time is 3: 40 H= 3 and M=40
Angle = |30 x 3 - $\frac{11}{2}$ x 40|
=|90-220| = 130^{0}

__Wipro Placement Papers with
Answers – Clocks Solved Question 5__
At what angle the
hands of a clock are inclined at 15 minutes past 5?

a) $\frac{117}{2}$ ° b)
64 ° c) $\frac{135}{2}$ ° d) $\frac{145}{2}$ °

Answer: C

Explanation :

The direct
formula to find the angle between two hands when the time in the clock is
H: M
Angle = |30H -$\frac{11}{2}$ M|
Here the given
time is 5: 15 H= 5 and M=15
Angle = |30 x 5 - $\frac{11}{2}$ x 15|
=|150 -87 ½| =
$\frac{135}{2}$ ^{0}

__Wipro Placement Questions with Explanations –
Model Question 6__
Find the angle
between the hour and the minute hand of a clock when the time is 3.25.

a) 47 ½ b)
49 ½ c) 55 ½ d) 57 ½
Answer: A
Explanation :

The direct
formula to find the angle between two hands when the time in the clock is H: M
Angle = |30H - $\frac{11}{2}$ M|
Here the given
time is 3: 25. H=3 and M=25
Angle =|( 30 x 3_ - ($\frac{11}{2}$ x 25)|
=|90 - 137.5|
= 47.5^{0
} or 47 $\frac{1}{2}$^{0}

__Wipro Latest Placement Papers – Model
Problems on Clocks 7__
At what time between
2 and 3 o'clock, will the hands of a clock be together?

a) 10 $\frac{10}{11}$ b)
10 11/10 c) 11 $\frac{10}{11}$ d)
12 $\frac{10}{11}$

Answer : A
Explanation:
Method 1:
At 2'O clock, the hour hand is at 2 and the minute hand is at 12. Hence minute hand is 10 minutes
spaces behind the hour hand.
The two hands will
coincide each other, when the minute hand gains 10 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 $\frac{60}{55}$ minutes.
To gain 20 minutes spaces,
it will take 10 x $\frac{60}{55}$ = 10 x $\frac{12}{11}$ =10 $\frac{10}{11}$ minutes
∴The two hands
coincide at 10 $\frac{10}{11}$ minutes past 2.
Method 2 :
When the two hands coincide, the angle
between the two hands is 0^{0}.
The angle between the two hands, when the
time in the clock is H:M is Angle = 30 H - $\frac{11}{2}$ M
Here
we take the first hour as H, and we have to find the value of M.
Angle = 30 H - $\frac{11}{2}$ M
0^{0}=
30 x 2 - $\frac{11}{2}$ x M
=>$\frac{11}{2}$ x M = 60
=> M = 60 x $\frac{2}{11}$ = 10 $\frac{10}{11}$ minutes
Therefore between 4 and 5 ‘O
clock, the two hands coincide at 2 : 10 $\frac{10}{11}$ minutes

__Wipro Placement Papers with
Answers – Model Questions 8__
At what time, in
minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each
other?

a) 5 $\frac{1}{11}$ ° b)
12 $\frac{4}{11}$° c) 13 $\frac{4}{11}$° d) 16 $\frac{4}{11}$°
Answer : C
Explanation :When the two hands coincide, the angle
between the two hands is 0^{0}.
The angle between the two hands, when the
time in the clock is H: M is

Angle = |30 H - $\frac{11}{2}$M|
Here
we take the initial hour as H, and we have to find the value of M.
Angle = |30 H - $\frac{11}{2}$ M|
0^{0}= |30 x 3 - $\frac{11}{2}$ x M|
Ã°
$\frac{11}{2}$ x M = 90
Ã° M = 90 x $\frac{11}{2}$= 16
$\frac{4}{11}$ minutes
Therefore between 4 and 5 ‘O
clock, the two hands coincide at 3:16 $\frac{4}{11}$ minutes

__Wipro
Latest Placement Questions - Model Problems on Clocks 9__
Imagine a railway station clock with the second-hand on the same
axis as the two other hands. How often in a 24-hour day, will the second-hand
be parallel to either of the two other hands?
a) 5474 b)
5174 c) 5714 d) 5724
Answer
: C
Explanation
:
In a 24-hour day, the
second-hand will be 5714 times parallel to the two other hands.

Within any minute, the second-hand will twice be
parallel to each of the two other hands, minute-hand and hour-hand.
Thus, there are
(4*60*24) 5760 such parallel positions in one day.

But, the hour-hand and
the minute-hand are parallel to each other 23 times in 12 hours i.e. 46 times
in 24 hours. Therefore, 46 parallel positions have to be deducted.
Hence, the correct
answer is (5760 - 46) = 5714
In 24-hours or a day, the seconds hand is parallel to either of the two hands 5714 times.

__Wipro Placement Papers with Answers – Model Problems
on Clocks 10__
At how many points
between 10 O'clock and 11 O'clock are the minute hand and the hour hand of a clock
at an angle of 30 degrees to each other?

a)1 b)2 c)3 d)4
Answer :A
Explanation :
Between 10 and 11, the minute hand
and hour hand are at an angle of 30^{o} to each at
Case 1 : When the minute hand is behind the hour hand
30^{0} = 30 x 10 – $\frac{11}{2}$ x m
Ã° M = $\frac{540}{11}$
Ã° 49 $\frac{11}{11}$ minutes past 10.
Case 2 : When the minute hand is
ahead of the hour hand
-30^{0} = 30 x 10 – $\frac{11}{2}$ M
Ã° M = $\frac{600}{11}$ = 60 minutes after 11
First time they are 30^{0}
apart at 49 $\frac{1}{11}$ minutes past 10.
The next time they will be at the angle of 30^{o} to each other will be at 11.
So only 1 time, it happens

__Latest Wipro Placement Questions– Model Problems on Clocks 11__
A Clock strikes every hour-once at 1.00, twice
at 2.00, and so on. The clock takes 6 seconds to strike 5.00 and 12 seconds to
strike 9.00. The time needed to strike 1.00 is negligible. How long does the
clock need for all its striking in 24 hours?

a)168 Seconds b)178
Seconds c)188 Seconds d) 198 Seconds
Answer :D
Explanation :

The clock takes 6 seconds s to strike 5.00.
So there are 4 interval gaps between 5 strikes.
So the gap between each striking is $\frac{6}{4}$ = 1.5 seconds.

To strike 2.00, it takes = 1.5 seconds.

To strike 3.00 ,it takes = 3 seconds.

To strike 4.00 ,it takes = 4.5 seconds

................

................

To strike 12.00, it takes = 16.5 seconds.

So it takes a total of 1.5 + 3 +
4.5 + . . . . . . + 16.5
= 1.5 ( 1 + 2 + 3 + .... + 11) = 99
seconds to strike 12 hours.

For 24 hours the clock takes 99 × 2 = 198
seconds

__Wipro
Latest Placement Questions– Model Problems On Clocks 12__
A watch which gains uniformly is 2 minutes slow
at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday.
When was it correct?

a) 2 p.m. on Tuesday b) 2 p.m. on Wednesday
c) 3 p.m. on Thursday d) 1 p.m. on Friday
Answer :B
Explanation :
Number of hours between noon (12 P.M) on
Monday to 2 p.m on the following Monday
= 1 Week + 2 hours = 170 hours
The clock gains 2
minutes + 4 minutes 48 seconds (4 $\frac{48}{60}$ minutes) in 170 hours
Thus the clock gains (2 + 4 $\frac{4}{5}$ min ) in 170 hours
i.e., the clock gains $\frac{34}{5}$
minutes in 170 hours
Now $\frac{34}{5}$ minutes are
gained in 170 hours
To be correct, it has to
gain 2 minutes from 12 p.m Saturday
∴ 2 min are gained 170 x $\frac{5}{34}$ x 2 =
50 hours = 2 days 2 hours
12 p.m Monday + 2 days
2 hours = 2 p.m. on Wednesday
The clock was correct at 2 p.m on
Wednesday.

A clock is set at 5 a.m. The clock loses 16
minutes in 24 hours. What will be the true time when the clock indicates 10
p.m. on 4th day?

a) 9 p.m b) 10 p.m c) 11 p.m d)
12 p.m

Answer: C
Explanation:

Total number of hours
from Today 5 a.m. to the 10 p.m. on the 4^{th} day
Ã° (24 hours x 3
days) + 17 = 59 hours
The clock loses
16 minutes in every 24 hours.
23 hours 44 min.
of this clock= 24 hours of the correct clock,
i.e. $\frac{356}{15}$
hours
of this clock = 24 hours of correct clock
∴ 89 hours of this clock =( 24 x $\frac{15}{356}$
x 89)
hours of correct clock
= 90 hours of the correct clock.
So the correct time is 1 hour more than 10 pm. i.e.,
11 pm.

__Wipro Placement Papers with Solutions –Problems on Clocks__

__1__
In a conventional clock, how many times does the minute hand pass the hour hand between noon and midnight?

a) 10 times b)11 times c)12
times d)15 times

Answer : A

Explanation :

In 12 hours, the hour hand goes around the
dial just once and the minute hand goes around 12 times.

Therefore they pass each other (12 – 1) = 11
times.

One of these 11 times is 12 midnight also.

But between noon and midnight is asked.

So we don’t count either noon or midnight

Therefore the answer is 10.

__Wipro Placement Questions with Answers – Problems on Clocks 2__
How many times in a
day, the hands of a clock are straight?

a) 22 b) 24 c) 44 d) 48

Answer : C

a) 22 b) 24 c) 44 d) 48

Answer : C

Explanation: Any relative
position of the two hands of a clock is repeated 11 times every 12 hours.

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

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

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

__Wipro Placement Papers with Answers – Clocks Solved Problem 3__
How many times do the hands of a
clock point towards each other in a day?

a)12 b)
18 c) 22 d)
24

Answer : C

Explanation :

In one hour, the two hands point
towards each other only once.

The hands of a
clock point towards each other 11 times in 12 hours. (Because between 5 O.’
clock and 7 O’ clock, at 6 O’clock only
they point towards each other)

In 12 hours, it happens 11 times.
Hence in a day ( 24 hours), 22 times.

So, in a day the two hands point
towards each other 22 times

__Wipro Placement Questions with Solutions – Model Problems on Clocks 4__
At 3.40, the hour
hand and the minute hand of a clock form an angle of

a) 120° b) 125° c) 130° d) 135°

Answer: C

Explanation :

The direct formula to find the angle between two hands when the time in the clock is

a) 120° b) 125° c) 130° d) 135°

Answer: C

Explanation :

The direct formula to find the angle between two hands when the time in the clock is

H: M

Angle = |30H -$\frac{11}{2}$
M|

Here the given
time is 3: 40 H= 3 and M=40

Angle = |30 x 3 - $\frac{11}{2}$ x 40|

=|90-220| = 130

^{0}

__Wipro Placement Papers with Answers – Clocks Solved Question 5__
At what angle the
hands of a clock are inclined at 15 minutes past 5?

a) $\frac{117}{2}$ ° b) 64 ° c) $\frac{135}{2}$ ° d) $\frac{145}{2}$ °

Answer: C

Explanation :

The direct formula to find the angle between two hands when the time in the clock is

a) $\frac{117}{2}$ ° b) 64 ° c) $\frac{135}{2}$ ° d) $\frac{145}{2}$ °

Answer: C

Explanation :

The direct formula to find the angle between two hands when the time in the clock is

H: M

Angle = |30H -$\frac{11}{2}$ M|

Here the given
time is 5: 15 H= 5 and M=15

Angle = |30 x 5 - $\frac{11}{2}$ x 15|

=|150 -87 ½| =
$\frac{135}{2}$

^{0}

__Wipro Placement Questions with Explanations – Model Question 6__
Find the angle
between the hour and the minute hand of a clock when the time is 3.25.

a) 47 ½ b) 49 ½ c) 55 ½ d) 57 ½

a) 47 ½ b) 49 ½ c) 55 ½ d) 57 ½

Answer: A

Explanation :

The direct formula to find the angle between two hands when the time in the clock is H: M

The direct formula to find the angle between two hands when the time in the clock is H: M

Angle = |30H - $\frac{11}{2}$ M|

Here the given
time is 3: 25. H=3 and M=25

Angle =|( 30 x 3_ - ($\frac{11}{2}$ x 25)|

=|90 - 137.5|

= 47.5

^{0 }or 47 $\frac{1}{2}$^{0}

__Wipro Latest Placement Papers – Model Problems on Clocks 7__
At what time between
2 and 3 o'clock, will the hands of a clock be together?

a) 10 $\frac{10}{11}$ b) 10 11/10 c) 11 $\frac{10}{11}$ d) 12 $\frac{10}{11}$

Answer : A

a) 10 $\frac{10}{11}$ b) 10 11/10 c) 11 $\frac{10}{11}$ d) 12 $\frac{10}{11}$

Answer : A

Explanation:

Method 1:

At 2'O clock, the hour hand is at 2 and the minute hand is at 12. Hence minute hand is 10 minutes
spaces behind the hour hand.

The two hands will
coincide each other, when the minute hand gains 10 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 $\frac{60}{55}$ minutes.

To gain 20 minutes spaces,
it will take 10 x $\frac{60}{55}$ = 10 x $\frac{12}{11}$ =10 $\frac{10}{11}$ minutes

∴The two hands
coincide at 10 $\frac{10}{11}$ minutes past 2.

Method 2 :

When the two hands coincide, the angle
between the two hands is 0

^{0}.
The angle between the two hands, when the
time in the clock is H:M is Angle = 30 H - $\frac{11}{2}$ M

Here
we take the first hour as H, and we have to find the value of M.

Angle = 30 H - $\frac{11}{2}$ M

0

^{0}= 30 x 2 - $\frac{11}{2}$ x M
=>$\frac{11}{2}$ x M = 60

=> M = 60 x $\frac{2}{11}$ = 10 $\frac{10}{11}$ minutes

Therefore between 4 and 5 ‘O
clock, the two hands coincide at 2 : 10 $\frac{10}{11}$ minutes

__Wipro Placement Papers with Answers – Model Questions 8__
At what time, in
minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each
other?

a) 5 $\frac{1}{11}$ ° b) 12 $\frac{4}{11}$° c) 13 $\frac{4}{11}$° d) 16 $\frac{4}{11}$°

a) 5 $\frac{1}{11}$ ° b) 12 $\frac{4}{11}$° c) 13 $\frac{4}{11}$° d) 16 $\frac{4}{11}$°

Answer : C

Explanation :When the two hands coincide, the angle
between the two hands is 0

^{0}.
The angle between the two hands, when the
time in the clock is H: M is

Angle = |30 H - $\frac{11}{2}$M|

Angle = |30 H - $\frac{11}{2}$M|

Here
we take the initial hour as H, and we have to find the value of M.

Angle = |30 H - $\frac{11}{2}$ M|

0

^{0}= |30 x 3 - $\frac{11}{2}$ x M|
Ã°
$\frac{11}{2}$ x M = 90

Ã° M = 90 x $\frac{11}{2}$= 16
$\frac{4}{11}$ minutes

Therefore between 4 and 5 ‘O
clock, the two hands coincide at 3:16 $\frac{4}{11}$ minutes

__Wipro Latest Placement Questions - Model Problems on Clocks 9__
Imagine a railway station clock with the second-hand on the same
axis as the two other hands. How often in a 24-hour day, will the second-hand
be parallel to either of the two other hands?

a) 5474 b)
5174 c) 5714 d) 5724

Answer
: C

Explanation
:

In a 24-hour day, the
second-hand will be 5714 times parallel to the two other hands.

Within any minute, the second-hand will twice be parallel to each of the two other hands, minute-hand and hour-hand.

Within any minute, the second-hand will twice be parallel to each of the two other hands, minute-hand and hour-hand.

Thus, there are
(4*60*24) 5760 such parallel positions in one day.

But, the hour-hand and
the minute-hand are parallel to each other 23 times in 12 hours i.e. 46 times
in 24 hours. Therefore, 46 parallel positions have to be deducted.

Hence, the correct
answer is (5760 - 46) = 5714

In 24-hours or a day, the seconds hand is parallel to either of the two hands 5714 times.

__Wipro Placement Papers with Answers – Model Problems on Clocks 10__
At how many points
between 10 O'clock and 11 O'clock are the minute hand and the hour hand of a clock
at an angle of 30 degrees to each other?

a)1 b)2 c)3 d)4

a)1 b)2 c)3 d)4

Answer :A

Explanation :

Between 10 and 11, the minute hand
and hour hand are at an angle of 30

^{o}to each at
Case 1 : When the minute hand is behind the hour hand

30

^{0}= 30 x 10 – $\frac{11}{2}$ x m
Ã° M = $\frac{540}{11}$

Ã° 49 $\frac{11}{11}$ minutes past 10.

Case 2 : When the minute hand is
ahead of the hour hand

-30

^{0}= 30 x 10 – $\frac{11}{2}$ M
Ã° M = $\frac{600}{11}$ = 60 minutes after 11

First time they are 30

^{0}apart at 49 $\frac{1}{11}$ minutes past 10.
The next time they will be at the angle of 30

^{o}to each other will be at 11.
So only 1 time, it happens

__Latest Wipro Placement Questions– Model Problems on Clocks 11__
A Clock strikes every hour-once at 1.00, twice
at 2.00, and so on. The clock takes 6 seconds to strike 5.00 and 12 seconds to
strike 9.00. The time needed to strike 1.00 is negligible. How long does the
clock need for all its striking in 24 hours?

a)168 Seconds b)178 Seconds c)188 Seconds d) 198 Seconds

a)168 Seconds b)178 Seconds c)188 Seconds d) 198 Seconds

Answer :D

Explanation :

The clock takes 6 seconds s to strike 5.00.

The clock takes 6 seconds s to strike 5.00.

So there are 4 interval gaps between 5 strikes.

So the gap between each striking is $\frac{6}{4}$ = 1.5 seconds.

To strike 2.00, it takes = 1.5 seconds.

To strike 3.00 ,it takes = 3 seconds.

To strike 4.00 ,it takes = 4.5 seconds

................

................

To strike 12.00, it takes = 16.5 seconds.

So it takes a total of 1.5 + 3 + 4.5 + . . . . . . + 16.5

To strike 2.00, it takes = 1.5 seconds.

To strike 3.00 ,it takes = 3 seconds.

To strike 4.00 ,it takes = 4.5 seconds

................

................

To strike 12.00, it takes = 16.5 seconds.

So it takes a total of 1.5 + 3 + 4.5 + . . . . . . + 16.5

= 1.5 ( 1 + 2 + 3 + .... + 11) = 99
seconds to strike 12 hours.

For 24 hours the clock takes 99 × 2 = 198 seconds

For 24 hours the clock takes 99 × 2 = 198 seconds

__Wipro Latest Placement Questions– Model Problems On Clocks 12__
A watch which gains uniformly is 2 minutes slow
at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday.
When was it correct?

a) 2 p.m. on Tuesday b) 2 p.m. on Wednesday

a) 2 p.m. on Tuesday b) 2 p.m. on Wednesday

c) 3 p.m. on Thursday d) 1 p.m. on Friday

Answer :B

Explanation :

Number of hours between noon (12 P.M) on
Monday to 2 p.m on the following Monday
= 1 Week + 2 hours = 170 hours

The clock gains 2
minutes + 4 minutes 48 seconds (4 $\frac{48}{60}$ minutes) in 170 hours

Thus the clock gains (2 + 4 $\frac{4}{5}$ min ) in 170 hours

i.e., the clock gains $\frac{34}{5}$
minutes in 170 hours

Now $\frac{34}{5}$ minutes are
gained in 170 hours

To be correct, it has to
gain 2 minutes from 12 p.m Saturday

∴ 2 min are gained 170 x $\frac{5}{34}$ x 2 =
50 hours = 2 days 2 hours

12 p.m Monday + 2 days
2 hours = 2 p.m. on Wednesday

The clock was correct at 2 p.m on
Wednesday.

A clock is set at 5 a.m. The clock loses 16
minutes in 24 hours. What will be the true time when the clock indicates 10
p.m. on 4th day?

a) 9 p.m b) 10 p.m c) 11 p.m d) 12 p.m

Answer: C

a) 9 p.m b) 10 p.m c) 11 p.m d) 12 p.m

Answer: C

Explanation:

Total number of hours from Today 5 a.m. to the 10 p.m. on the 4

Total number of hours from Today 5 a.m. to the 10 p.m. on the 4

^{th}day
Ã° (24 hours x 3
days) + 17 = 59 hours

The clock loses
16 minutes in every 24 hours.

23 hours 44 min.
of this clock= 24 hours of the correct clock,

i.e. $\frac{356}{15}$
hours
of this clock = 24 hours of correct clock

∴ 89 hours of this clock =( 24 x $\frac{15}{356}$
x 89)
hours of correct clock

= 90 hours of the correct clock.

So the correct time is 1 hour more than 10 pm. i.e.,
11 pm.