PE 1 - Clocks | Clocks & Calendars
What is the angle between the two hands of a clock at 6’O clock?
- A.
100°
- B.
180°
- C.
90°
- D.
None of these
Answer: Option B
Explanation :
At 6’O clock the hands of the clock are exactly opposite to each other.
∴ The angle between the hands will be 180°.
Hence, option (b).
Workspace:
What is the angle between the two hands of a clock at 3’O clock?
- A.
100°
- B.
180°
- C.
90°
- D.
None of these
Answer: Option C
Explanation :
At 3’O clock the hands of the clock are exactly perpendicular to each other.
∴ The angle between the hands will be 90°.
Hence, option (c).
Workspace:
What is the angle between the two hands of a clock at 4’O clock?
- A.
120°
- B.
180°
- C.
90°
- D.
None of these
Answer: Option A
Explanation :
The clock can be divided into 12 sectors of 30° each. (A sector would cover the area between any two consecutive numbers and the center.)
At 4’O clock the area between the two hands would cover 4 such sectors.
∴ The angle between the hands will be 4 × 30° = 120°.
Hence, option (a).
Workspace:
What is the angle between the two hands of a clock at 4 : 30?
- A.
37.5°
- B.
47.5°
- C.
50°
- D.
45°
Answer: Option D
Explanation :
At 4:30 the minute hand points towards 6, while the hour hand will be exactly between 4 and 5.
∴ The angle between the two hands will be equivalent to that of one and a half sector.
∴ Angle between the two hands = 1.5 × 30° = 45°
Alternately,
Angle between the two hands at h : m =
∴ At 4 : 30 the angle will be = = |120 – 165| = 45°.
Hence, option (d).
Workspace:
What is the angle between the two hands of a clock at 6 : 40?
- A.
37.5°
- B.
47.5°
- C.
40°
- D.
45°
Answer: Option C
Explanation :
Angle between the two hands at h : m =
∴ At 6 : 40 the angle will be = = |180 – 220| = 40°.
Hence, option (c).
Workspace:
What is the angle between the two hands of a clock at 9 : 20?
- A.
180°
- B.
160°
- C.
140°
- D.
150°
Answer: Option B
Explanation :
Angle between the two hands at h : m =
∴ At 9 : 20 the angle will be = = |270 – 110| = 160°.
Hence, option (b).
Workspace:
At what time between 7 and 8 will the hands of a clock be in the same straight line, but not together?
- A.
5 minutes past 7
- B.
5 minutes past 7
- C.
5 minutes past 7
- D.
5 minutes past 7
Answer: Option D
Explanation :
Hands should be in straight line but not together ⇒ hands should be opposite each other.
Angle between the two hands at h : m = || = 180°.
Between 7 and 8, h = 7.
∴ || = 180°
⇒ || = 180°
⇒ 210 - m = ± 180°
Case 1: 210 - m = 180°
⇒ m = 30°
⇒ m = 60/11 minutes = 5 minutes
∴ Hands will be opposite at 5 minutes past 7.
Case 2: 210 - m = - 180°
⇒ m = 370°
⇒ m = (not possible since m should be ≤ 60).
Hence, option (d).
Workspace:
How many times do the hands of a clock overlap each other in a day?
- A.
24
- B.
20
- C.
12
- D.
22
Answer: Option D
Explanation :
Hands of a clock overlap once every hour except between 11 and 1 O’clock when they overlap only once in these 2 hours (at 12 O'clock).
∴ The hands of a clock overlap 11 times in every 12 hours.
∴ So, in a day the hands overlap 22 times.
Hence, option (d).
Workspace:
How many times do the hands of a clock are opposite to each other in a day?
- A.
24
- B.
20
- C.
12
- D.
22
Answer: Option D
Explanation :
Hands of a clock are opposite to each other once every hour except between 5 and 7 O’clock when they are opposite only once in these 2 hours (at 6 O'clock).
∴ The hands of a clock are opposite 11 times in every 12 hours.
∴ So, in a day the hands are opposite 22 times.
Hence, option (d).
Workspace:
How many times are the hands of a clock at right angles in a day?
- A.
24
- B.
48
- C.
22
- D.
44
Answer: Option D
Explanation :
Hands of a clock are perpendicular twice every hour except between 2 - 4 O’clock and 8 – 10 O’clock when they are perpendicular thrice in there 2 hours.
∴ In 12 hours they are at right angles 22 times (because two positions 3 O'clock and 9 O'clock are common)
∴ In a day they are at right angle 44 times.
Hence, option (d).
Workspace:
At what time between 3 O'clok and 4 O'clock will the hands of a clock overlap?
- A.
3 : 15
- B.
3 : 20
- C.
3 : 4
- D.
3 : 16
Answer: Option D
Explanation :
Hands overlap when the angle between the two hands is 0°.
We know, angle between the hands of a clock (θ°) = |
⇒ 0° = |
⇒ 0° = 90 - m
⇒ m = = 16minutes
∴ The hands will coincide at 3 : 16.
Hence, option (d).
Workspace:
At what time between 7 O'clok and 8 O'clock will the hands of a clock be at an angle of 50°?
- A.
7 : 47
- B.
7 : 43
- C.
7 : 29
- D.
Both (a) and (c)
Answer: Option D
Explanation :
We know, angle between the hands of a clock (θ°) = |
⇒ 50° = |
Case 1:
⇒ 50° = 210 - m
⇒ m = 160°
⇒ m = = 29minutes
∴ The hands will be at an angle of 50° at 7 : 29.
Case 2:
⇒ -50° = 210 - m
⇒ m = 260°
⇒ m = = 47minutes
∴ The hands will be at an angle of 50° at 7 : 47.
Hence, option (d).
Workspace:
At what time between 10 O'clok and 11 O'clock will the hands of a clock be at an angle of 69°?
- A.
10 : 41
- B.
10 : 67
- C.
10 : 57
- D.
Both (b) and (c)
Answer: Option B
Explanation :
We know, angle between the hands of a clock (θ°) = |
⇒ 69° = |
Case 1:
⇒ 69° = 300 - m
⇒ m = 231°
⇒ m = 42 minutes
∴ The hands will be at an angle of 69° at 10 : 42.
Case 2:
⇒ -69° = 300 - m
⇒ m = 369°
⇒ m = = 67minutes
∴ The hands will be at an angle of 69° at 10 : 67.
Hence, option (b).
Workspace:
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