Q 1-A clock is started at noon. By 10 minutes past 5, the hour hand has turned through

A - 155°

B - 145°

C - 152°

D - 140°

Answer - A

Explanation

"We know that Angle traced by hour hand in 12 hrs = 360° 

Time duration from noon to 10 minutes past 5 
= 5 hours 10 minutes=5(10/60) hour
=31/6hours 

Hence the angle traced by hour hand from noon to 10 minutes past 5 

= [31/6] × [360/12]

=[31/6] × 30
=31 × 5=155°
"

Q 2-At what time between 5 and 6 o'clock are the hands of a clock 3 min apart?

A - 346/11 min. past 5

B - 350/11 min. past 5

C - 352/11 min. past 5

D - 356/11 min. past 5

Answer - A

Explanation

"At 5 o'clock, the minute hand is 25 min. spaces behind the hour hand.
Case I. Minute hand is 3 min. spaces behind the hour hand.

In this case, the minute hand has to gain' (25 - 3) = 22 minute spaces.
55 min. are gained in 60 min.

22 min. are gaining in (60*22)/55min. = 24 min.

The hands will be 3 min. apart at 24 min. past 5.

Case II. Minute hand is 3 min. spaces ahead of the hour hand.

In this case, the minute hand has to gain (25 + 3) = 28 minute spaces.

55 min. are gained in 60 min.

28 min. are gained in (60 x 28)/55 = 346/11

The hands will be 3 min. apart at 346/11 min. past 5.
"

Q 3-How many times will the hands of a clock coincide in a day?

A - 24

B - 22

C - 20

D - 21

Answer - A

Explanation

"The hands of a clock coincide 11 times in every 12 hours 
(Between 11 and 1, they coincideonly once, at 12 o'clock).
 12:00 am ,1:05 am ,2:11 am, 3:16 am, 4:22 am,5:27 am,
6:33 am,7:38 am,8:44 am,9:49 am,10:55 am,12:00 pm,
1:05 pm,2:11 pm,3:16 pm,4:22 pm,5:27 pm,6:33 pm,
7:38 pm,8:44 pm,9:49 pm,10:55 pm 
Hence the hands coincide 22 times in a day.
"

Q 4-Find the time between 4 and 5'o clock, when the two hands of a clock are 4 minutes apart?

A - 26(2/11) minutes past 4 and 17(5/11) minutes past 4

B - 26(1/11) minutes past 4 and 17(5/11) minutes past 4

C - 26(2/11) minutes past 4 and 17(4/11) minutes past 4

D - 26(1/11) minutes past 4 and 17(4/11) minutes past 4

Answer - A

Explanation

"Between H and (H + 1) o'clock,
 the two hands of a clock are M minutes apart at(5H±M)12/11minutes past H 'o clock 
Here H=4 and M=4.
 Hence the two hands are 4 minutes apart 
between 4 and 5 at([5×4]±4)12/11minutes past 4 'o clock =(20±4)12/11minutes past 4 'o clock =[16×12]/11minutes past 4 'o clock
 and [24×12]/11minutes past 4 'o clock =192/11minutes past 4 'o clock
 and 288/11minutes past 4 'o clock 
=17(5/11)minutes past 4 'o clock and 26(2/11)minutes past 4 'o clock
"

Q 5-What is the reflex angle between the hands of a clock at 10.25?

A - 195°

B - 197(1/2)°

C - 180°

D - 193(1/2)°

Answer - B

Explanation

"Angle between Hands of a clock

When the minute hand is behind the hour hand,
 the angle between the two hands at M minutes past H'o clock
=30(H−[M/5[)+[M/2] degree

When the minute hand is ahead of the hour hand,
 the angle between the two hands at M minutes past H'o clock
=30([M/5]−H)−[M/2] degree

Here H = 10 , M = 25 and the minute hand is behind the hour hand. Hence the angle

  
=30(H−[M/5])+[M/2]
=30(10−[25/5])+[25/2]
=30(10−5)+12.5
=30×5+12.5=150+12.5
=162.5°
=30(H−[M/5])+[M/2]

=30(10−[25/5])+[25/2]
=30(10−5)+12.5
=30×5+12.5
=150+12.5=162.5°

==>  Reflex angle = 360 - 162.5 = 197.5 °
"

Q 6-The angle between the minute hand and the hour hand of a clock when the time is 4.20 is

A - 10°

B - 5°

C - 0°

D - 1°

Answer - A

Explanation

"4 hour 20 minutes = 4(1/3)hour=13/3hour

Angle traced by hour hand in 12 hrs = 360°

  
Angle traced by hour hand in 133 hour = [360/12]×[13/3]
=30×[13/3]
=10×13=130°

Angle traced by minute hand in 60 min. = 360°.

  
Angle traced by minute hand in 20 min. = [360/60]×20
=6×20=120°. 

Angle between the hands of the clock when the time is 4.20 = 
130° - 120° =10°."

Q 7-A watch which gains uniformly is 2 minutes low at noon on and is 4 min 48 sec fast at 2 pm on the following Monday. When was it correct?

A - 2 pm on Tuesday

B - 3 pm on Wednesday

C - 2 pm on Wednesday

D - 3 pm on Tuesday

Answer - C

Explanation

"Time from Monday noon (12 o'clock) to following Monday 2 pm = 7 day 2 hours 

=7×24+2=168+2=170 hours =7×24+2=168+2=170 hours 

Total time gained Monday noon (12 o'clock) to following Monday 2 pm = 2 min + 4 min 48 sec
  
= 6 min 48 sec = 6(48/60) mins = 6(4/5) mins 
= 34/5 mins
  
=> The given watch gains 34/5 mins in 170 hours 

Given that the said watch was 2 minutes low at Monday noon.
 
Hence when it gained 2 minutes,the time was correct.
    
The given watch gains 34/5 mins in 170 hours

=> The given watch gains 2 mins in 170×5/34]×2 hours

=5×5×2 hours = 50 hours

 Hence the time was correct after 50 hours from Monday noon 
= after 2 days 2 hours from Monday noon 
=2 pm on Wednesday
"

Q 8-A watch which gains uniformly, is 6 min. slow at 8 o'clock in the morning Sunday and it is 6 min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct?

A - 20 min. past 7 p.m. on Tuesday

B - 20 min. past 7 p.m.on Wednesday

C - 20 min. past 7 p.m. on Thursday

D - 20 min. past 7 p.m. on Friday

Answer - B

Explanation

"Time from 8 a.m. on Sunday to 8 p.m. on following Sunday 
= 7 days 12 hours = 180 hours

The watch gains (5 + 29/5) min. or 54/5 min. in 180 hrs.
Now 54/5 min. are gained in 180 hrs.

5 min. are gained in (180 x 5/54 x 5) hrs = 83 hrs 20 min. 
= 3 days 11 hrs 20 min.

Watch is correct 3 days 11 hrs 20 min. 
after 8 a.m. of Sunday.

It will be correct at
20 min. past 7 p.m. on Wednesday.
"

Q 9-The minute hand of a clock overtakes the hour hand at intervals of 65 minutes. How much a day does the clock gain or loss?

A - 10(9/143) minutes

B - 11(9/143) minutes

C - 11(10/143) minutes

D - 10(10/143) minutes

Answer - D

Explanation

"The minute hand of a clock overtakes the hour hand 
at intervals of M minutes of correct time.

The clock gains or loses in a day by

=([720/11]−M)/([60×24] / M) minutes

Here M = 65. 

The clock gains or losses in a day by

=([720/11]−M)/([60×24]/M)
=([720/11]−65)/([60×24]/65)
=[5/11]  X ([12×24]/13)
=1440/143
=10(10/143) minutes
"

Q 10-The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:

A - 80º

B - 75º

C - 60º

D - 105º

Answer - B

Explanation

"Angle traced by hour hand in 17/2 hrs. = ([360/12) X [17/2]) º= 255º.
Angle traced by hour hand in 30 mins = ([360/12) X [30]) º = 180 º
Therefore
Required angle = (255 º - 180 º)= 75 º ."

Q 11-At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?

A - 5 minutes past 7

B - 5(3/11) miinutes past 7

C - 5(1/11) minutes past 7

D - 5(5/11) minutes past 7

Answer - D

Explanation

"If the hands of the clock are in the same straight line,
 but not together, they will be 30 minutes apart.

  At 7'o clock, the hands of the clock are 25 minutes apart.
  Hence the minute hand should 
  gain 5 minutes so that the hands will be 30 minutes apart
We know that, in 60 minutes, the minute hand gains 
55 minutes on the hour on the hour hand.
Hence to gain 5 minutes for the minute hand, 

time needed = [60/55] × 5=60/11 minutes = 5(5/11) minutes

That means when the time is 5511 minutes past 7, 
the hands of a clock will be in the same straight line but, not together
"

Q 12-A clock strikes 4 taking 9 seconds. In order to strike 12 at the same rate, the time taken is

A - 33 seconds

B - 30 seconds

C - 36 seconds

D - 27 seconds

Answer - A

Explanation

"There are 3 intervals when the clock strikes 4

Time taken at 3 intervals = 9 seconds

Time taken for 1 interval = 9/3 =3 seconds

In order to strike 12, there are 11 intervals. Hence time needed 

=3*11=33 seconds
"

Q 13-At what time between 4 and 5 o'clock will the hands of a clock be at right angle?

A - 40/11 min. past 4

B - 45/11 min. past 4

C - 50/11 min. past 4

D - 60/11 min. past 4

Answer - A

Explanation

"At 4 o'clock, the minute hand will be 20 min.
 spaces behind the hour hand

Now, when the two hands are at right angles, 
they are 15min. spaces apart.
So, they are at right angles in following two cases.

Case I. When minute hand is 15 min. spaces behind the hour hand:
In this case min. hand will have to gain (20 - 15) = 5 minute spaces. 

55 min. spaces are gained by it in 60 min.

5 min spaces will be gained by it in 60*5/55 min=60/11min.
They are at right angles at 60/11min. past 4.

Case II. When the minute hand is 15 min. spaces ahead of the hour hand:

To be in this position, the minute hand will have to gain (20 + 15) 
= 35 minute spaces.

55 min. spaces are gained in 60 min.

35 min spaces are gained in (60 x 35)/55 min =40/11

They are at right angles at 40/11 min. past 4.
"

Q 14-A clock is set at 5 am. If the clock loses 16 minutes in 24 hours, what will be the true time when the clock indicates 10 pm on 4th day?

A - 9.30 pm

B - 10:00 PM

C - 10.30 pm

D - 11:00 PM

Answer - D

Explanation

"Time from 5 am to 10 pm on the 4th day = 3 days 17 hours 
= 3×24+17=89 hours
Given that clock loses 16 minutes in 24 hours
⇒23 hour 44 minutes of the given clock
 = 24 hours in a normal clock
⇒23(44/60) hours of the given clock 
= 24 hours in a normal clock
⇒23(11/15) hours of the given clock = 24 hours in a normal clock
⇒356/15 hours of the given clock = 24 hours in a normal clock
⇒89 hours of the given clock = 24×(15/356)×89 hours in a normal clock
=(24×15)/4=6×15=90 hours
So the correct time is 90 hours after 5 am 
= 3 days 18 hours after 5 am 
= 11 pm on the 4th day
"

Q 15-At what time between 5 and 6 'o clock, will the hands of a clock be at right angle?

A - 10(10/11) minutes past 5 and 43(7/11) minutes past 5

B - 10(10/11) minutes past 5 and 42(7/11) minutes past 5

C - 10(9/11) minutes past 5 and 42(7/11) minutes past 5

D - 10(9/11) minutes past 5 and 42(7/11) minutes past 5

Answer - A

Explanation

"At 5, the hands are 25 minutes spaces apart
to get first right angle ,
the minute hand has to gain 25 - 15 = 10 minutes
To get second right angle ,
the minute hand has to gain 25 + 15 = 40 minutes

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

To gain 10 minutes for the minute hand, time needed 

=[60/55×10]=[12/11]×10=120/11=10(10/11) minutes

To gain 40 minutes for the minute hand, time needed 

= [60/55]×40=[12/11]×40=480/11=43(7/11) minutes

That means when the time is 10(10/11) minutes past 5 and 43(7/11) minutes past 5,
the hands of a clock will be at right angles
"

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