Answer: Option D. -> $MF#%47\dfrac{1}{2}$MF#%

Answer : Option D

Explanation :

$MF#%\boxed{\begin{align} &\text{Angle between Hands of a clock}\\\\\\\\ &\text{When the minute hand is behind the hour hand, the angle}\\ &\text{between the two hands at M minutes past H'o clock}\\ &= 30\left(H - \dfrac{M}{5}\right) + \dfrac{M}{2}\text{ degree}\\\\\\\\\\\ &\text{When the minute hand is ahead of the hour hand, the angle}\\ &\text{between the two hands at M minutes past H'o clock}\\ &= 30\left(\dfrac{M}{5} - H\right) - \dfrac{M}{2}\text{ degree}\end{align}} $MF#%

Here H = 3, M = 25 and the minute hand is ahead of the hour hand. Hence the angle

$MF#%= 30\left(\dfrac{M}{5} - H\right) - \dfrac{M}{2} = 30\left(\dfrac{25}{5} - 3\right) - \dfrac{25}{2} = 30\left(5 - 3\right) - 12.5\\\\ = 30 \times 2 - 12.5 = 60 - 12.5 = 47.5 °$MF#%

--------------------------------------------------------------------------------------- Solution 2 --------------------------------------------------------------------------------------- Its better to use formula as it can save lots of time in exams. However we should understand
the basics for sure. Please find the method given below to solve the same problem in
the traditional way.

$MF#%\text{3 hour 25 minutes = }3\dfrac{25}{60} hour = 3\dfrac{5}{12} hour = \dfrac{41}{12} hour$MF#%

Angle traced by hour hand in 12 hrs = 360°

$MF#%\text{Angle traced by hour hand in }\dfrac{41}{12}\text{ hour = }\dfrac{360}{12} \times \dfrac{41}{12} = 30 \times \dfrac{41}{12}\\\\ = 10 \times \dfrac{41}{4} = 10 \times 10.25 = 102.5°$MF#%

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

$MF#%\text{Angle traced by minute hand in 25 min. = }\dfrac{360}{60} \times 25 = 6 \times 25 = 150 °.
$MF#%

Angle between the hands of the clock when the time is 10.25 = 150° - 102.5° = 47.5 °.

Answer: Option A. -> 33 seconds

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

Answer: Option A. -> 40/11 min. past 4

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.

Answer: Option D. -> 180°

Angle traced by the hour hand in 6 hours =

360
x 6

°
= 180°.
12

Answer: Option B. -> 4 p.m.

Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. =
37
hrs.
4

3 min. 5 sec. of this clock = 3 min. of the correct clock.

37
hrs of this clock =
1
hrs of the correct clock.
720
20

37
hrs of this clock =

1
x
720
x
37

hrs of the correct clock.
4
20
37
4

      = 9 hrs of the correct clock.

The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.

Answer: Option D. -> 197 1 ° 2

Angle traced by hour hand in
125
hrs =

360
x
125

°
= 312
1
°
.
12
12
12
2

Angle traced by minute hand in 25 min =

360
x 25

°
= 150°.
60

Reflex angle = 360° -

312
1
- 150

°
= 360° - 162
1
°
= 197
1°
.
2
2
2

Answer: Option C. -> 155°

Angle traced by hour hand in 12 hrs = 360°.

Angle traced by hour hand in 5 hrs 10 min. i.e.,
31
hrs =

360
x
31

°
= 155°.
6
12
6

Answer: Option A. -> 32 8 min. 11

55 min. spaces are covered in 60 min.

60 min. spaces are covered in

60
x 60
min.
= 65
5
min.
55
11

Loss in 64 min. =

65
5
- 64

=
16
min.
11
11

Loss in 24 hrs =

16
x
1
x 24 x 60
min.
=
32
8
min.
11
64
11

Answer: Option D. -> 16 4 " 11

At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.

To be coincident, it must gain 15 min. spaces.

55 min. are gained in 60 min.

15 min. are gained in

60
x 15
min
=
16
4
min.
55
11

The hands are coincident at 16
4
min. past 3.
11

Answer: Option C. -> 22

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).

AM

12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

PM

12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

The hands overlap about every 65 minutes, not every 60 minutes.

The hands coincide 22 times in a day.