Q 1-How much does a watch lose per day, if it's hands coincide every 64 minutes?

A - [32x8] / 11 min

B - [36x8] / 11 min

C - 90 min

D - 96 min

Answer - A

Explanation

"55 min. spaces are covered in 60 min.

60 min. spaces are covered

in (60/55 x 60) min=65x5/11 min.

Loss in 64 min.([65x5] / 11-64)=16/11
Loss in 24 hrs([16/11x1] / [64x24x60])min=32x8/11.
"

Q 2-At what angle the hands of a clock are inclined at 15 minutes past 5?

A - 67(1/2)°

B - 62(1/2)°

C - 70°

D - 63(3/4)°

Answer - A

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 = 5, M = 15 and the minute hand is behind the hour hand. Hence the angle

  
=30(H−[M/5])+M/2
=30(5−[15/5])+15/2
=30(5−3)+7.5
=30×2+7.5
=67.5°
"

Q 3-At what time between 8 and 9 o'clock will the hands of a clock are in the same straight line but not together?

A - 11(8/11) minutes past 8

B - 10(8/11) minutes past 8

C - 11(10/11) minutes past 8

D - 10(10/11) minutes past 8

Answer - D

Explanation

"The two hands of a clock will be in the same straight line 
but not together between H and (H + 1) o'clock at

 (5H−30)12/11 minutes past H, when H > 6
(5H+30)12/11 minutes past H, when H <6

Here H = 8. 
Hands of the clock will point in opposite directions at (5×8−30)12/11 minutes past 

8=10×[12/11]minutes past 8

=120/11 minutes past 8

=10(10/11)minutes past 8

"

Q 4-Find the angle between the hour hand and the minute hand of a clock when 3.25.

A - 91/2

B - 93/2

C - 95/2

D - 97/2

Answer - C

Explanation

"Angle traced by the hour hand in 12 hours = 360°

Angle traced by it in three hours 25 min (i.e.) 41/12 hrs = (360*[41/12]*12)°=205/2°

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

Angle traced by it in 25 min. = (360 X 25 )/60= 150°

Required angle = 150-205/2°= 95/2°

"

Q 5-At 3.40, the hour hand and the minute hand of a clock form an angle of

A - 135°

B - 130°

C - 120°

D - 125°

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 = 3, M = 40 and minute hand is ahead of the hour hand. Hence the angle

  
=30([M/5]−H)−M/2
=30([40/5]−3)−40/2
=30(8−3)−20
=30×5−20=130°

"

Q 6-How many times in a day, the hands of a clock are straight

A - 22

B - 44

C - 48

D - 24

Answer - B

Explanation

"The hands of a clock point in opposite directions 
(in the same straight line, making an 
angle 180° between them) 11 times in every 12 hours because between 5 and 7
 they point in opposite directions at 6 'o'clock only. 
Hence the hands point in the opposite directions 22 times in a day

The hands of a clock coincide(0° between them) 11 times in every 12 hours 
(Between 11 and 1, they coincide only once, at 12 o'clock). 
Hence the hands coincide 22 times 
in a day.

So In 24 hours, the hands come in opposite direction or coincide 44 times .

However this is already given as a formula and it's is better to by heart the answer as 44

which can save time in competitive exams.(However if you should know the theory behind)
"

Q 7-At what time between 6 and 7 will the hands be perpendicular

A - 48(1/11) minutes past 6 and 16(4/11) minutes past 6

B - 48 minutes past 6 and 16(3/11) minutes past 6

C - 49(1/11) minutes past 6 and 16(4/11) minutes past 6

D - 48(2/11) minutes past 6 and 16(3/11) minutes past 6

Answer - C

Explanation

"It's better to use formula as it can save lots of time in exams.
 However it's better tounderstand the basics. 
Please find the method given below to solve the same problem in

the traditional way.


At 5 o'clock, the hands are 30 minute spaces apart


Hence minute hand needs to gain 15 more minute spaces  
or 45 more minute spaces

so that the hands will be in right angles (90° between them)


We know that 55 min spaces are gained by minute hand in 60 min
 (with respect to hour hand) 


Hence time taken for gaining 15 minute spaces by minute hand

=[60/55] ⋅ 15=[12/11] ⋅ 15=[180/11]=16(4/11) minutes 


Hence time taken for gaining 45 minute spaces by minute hand


= [60/55] ⋅ 45=[12/11] ⋅ 45=[540/11] = 49(1/11) minutes 


Hence the hands will be perpendicular at 
16(4/11) minutes past 6 and 49(1/11) minutes past 6

"

Q 8-At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?

A - 53(6/11) minutes past 4

B - 53(7/11) minutes past 4

C - 54(6/11) minutes past 4

D - 54(7/11) minutes past 4

Answer - C

Explanation

"At 4 o'clock, the hands are 20 minute spaces apart
Hence minute hand needs to gain 50 more minute spaces 
so that the hands will
 point in opposite directions.

 We know that 55 min spaces are gained by minute hand 
 in 60 min (with respect to hour hand)

 Hence time taken for gaining 50 minute spaces by minute hand
  
=[60/55] × 50 minute=[12/11] × 50 minute=600/11minute=54(6/11) minute

Hence hands will point in opposite directions at 54(6/11) minute past 4
"

Q 9-A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is

A - 3:00 PM

B - 3.45 pm

C - 3.30 pm

D - 4:00 PM

Answer - D

Explanation

"Time from 7 am to 4.15 pm = 9 hours 15 minutes
= 9(1/4) hours=37/4 hours
3 minute 5 seconds of the given clock= 3 minutes of a normal clock
⇒3(1/12) minutes of the given clock = 3 minutes of a normal clock
⇒37/12 minutes of the given clock = 3 minutes of a normal clock
⇒37/720 hours of the given clock = 3/60 hours of a normal clock
⇒37/720 hours of the given clock = 120 hours of a normal clock
⇒37/4 hours of the given clock = 120×[720/37]×37/4 hours of the given clock
= 9 hours of the given clock
Hence the correct time = 9 hours after 7 am = 4 pm
"

Q 10-At what time between 5 and 6 will the hands of the clock coincide?

A - 26(2/11)minutes past 5

B - 26(3/11) minutes past 5

C - 28(3/11) minutes past 5

D - 27(3/11) minutes past 5

Answer - D

Explanation

"The two hands of a clock will be together between 
H and (H+1) o'clock at (60H/11)minutes past H o'clock.

Here H = 5.
 Hands will be together at (60 X 5)11minutes past 5
=[300/11]minutes past 5
=27(3/11)minutes past 5
"

Q 11-How many times in a day, are the hands of a clock in straight line but opposite in direction?

A - 20

B - 22

C - 24

D - 48

Answer - B

Explanation

"The hands of a clock point in opposite directions

(in the same straight line) 11 times in every 12 hours.
 
(Because between 5 and 7 they point in opposite directions at 6 o'clock only).

So, in a day, the hands point in the opposite directions 22 times."

Q 12-What is the angle between the hands at 4.40?

A - 95°

B - 100°

C - 120°

D - 110°

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 = 4, M = 40 
the minute hand is ahead of the hour hand. 
Hence the angle 30((M/5)−H)−[M/2] 
=30((40/5)−4)−[40/2] 
=30(8−4)−20 =30⋅4−20=100°
"

Q 13-How many times are the hands of a clock at right angle in a day?

A - 48

B - 44

C - 24

D - 22

Answer - B

Explanation

"In 12 hours, hands of a clock are at right angles at 22 times.

In 24 hours, hands of a clock are at right angles at 44 times."

Q 14-At what time between 2 and 3 o'clock will the hands of a clock be together?

A - 115/11 min. past 2

B - 120/11 min. past 2

C - 125/11 min. past 2

D - 130/11 min. past 2

Answer - B

Explanation

"At 2 o'clock, the hour hand is at 2 and the minute hand is at 12, 
i.e. they are 10 min spaces apart.

To be together, the minute hand must gain 10 minutes over the hour hand.

Now, 55 minutes are gained by it in 60 min.

10 minutes will be gained in (60 x 10)/55 min. = 120/11 min.

The hands will coincide at 120/11 min. past 2.
"

Q 15-An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

A - 154°

B - 180°

C - 170°

D - 160°

Answer - B

Explanation

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

From 8 to 2, there are 6 hours

The angle traced by the hour hand in 6 hours = 6×[360/12]=180°

"

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