Clocks in logical reasoning involve solving problems related to time, including calculating angles between clock hands, determining the time after a certain duration, and finding the time when given a specific angle between the hands of a clock.

Concept Explanation:

Clock Basics: A clock has two hands - an hour hand and a minute hand. The hour hand completes one full rotation in 12 hours, while the minute hand completes one full rotation in 60 minutes.

Calculating Angles: The angle between the hour and minute hands can be calculated using the formula:

Where Hour is the hour (1 to 12) and Minutes is the minutes (0 to 59).

Time Calculation: To calculate the time after a certain duration, you add the given duration to the current time.

Converting Angles to Time: To find the time when given a specific angle between the hands of a clock, you can use the formula:

Example:

Problem: What is the angle between the hour and minute hands of a clock at 3:20?

Solution: Using the formula,

__Multiple Choice Questions:__

1. What is the angle between the hour and minute hands of a clock at 6:30?

A) 15 degrees

B) 30 degrees

C) 45 degrees

D) 60 degrees

Answer: C) 45 degrees

2. If the time now is 3:45 pm, what will be the time 13 hours later?

A) 4:45 am

B) 4:45 pm

C) 5:45 am

D) 5:45 pm

Answer: D) 5:45 am

3. What is the angle between the hour and minute hands of a clock at 9:15?

A) 30 degrees

B) 45 degrees

C) 60 degrees

D) 75 degrees

Answer: D) 75 degrees

4. If the time now is 8:20 am, what will be the time 3 hours and 45 minutes later?

A) 11:05 am

B) 12:05 pm

C) 12:05 am

D) 1:05 pm

Answer: A) 11:05 am

5. What is the angle between the hour and minute hands of a clock at 4:50?

A) 100 degrees

B) 105 degrees

C) 110 degrees

D) 115 degrees

Answer: B) 105 degrees

6. If the time now is 2:30 pm, what will be the time 5 hours and 45 minutes later?

A) 8:15 pm

B) 8:15 am

C) 9:15 pm

D) 9:15 am

Answer: A) 8:15 pm

7. What is the angle between the hour and minute hands of a clock at 8:40?

A) 140 degrees

B) 145 degrees

C) 150 degrees

D) 155 degrees

Answer: C) 150 degrees

8. If the time now is 5:25 am, what will be the time 4 hours and 30 minutes later?

A) 9:55 am

B) 9:55 pm

C) 10:55 am

D) 10:55 pm

Answer: C) 10:55 am

9. What is the angle between the hour and minute hands of a clock at 10:10?

A) 45 degrees

B) 50 degrees

C) 55 degrees

D) 60 degrees

Answer: B) 50 degrees

10. If the time now is 11:15 pm, what will be the time 6 hours and 45 minutes later?

A) 6:00 am

B) 6:00 pm

C) 5:00 am

D) 5:00 pm

Answer: A) 6:00 am

11. What is the angle between the hour and minute hands of a clock at 1:50?

A) 125 degrees

B) 130 degrees

C) 135 degrees

D) 140 degrees

Answer: B) 130 degrees

12. If the time now is 6:45 pm, what will be the time 2 hours and 30 minutes later?

A) 9:15 pm

B) 9:15 am

C) 8:15 pm

D) 8:15 am

Answer: A) 9:15 pm

13. What is the angle between the hour and minute hands of a clock at 7:20?

A) 70 degrees

B) 75 degrees

C) 80 degrees

D) 85 degrees

Answer: B) 75 degrees

14. If the time now is 4:30 am, what will be the time 3 hours and 15 minutes later?

A) 7:45 am

B) 7:45 pm

C) 8:45 am

D) 8:45 pm

Answer: A) 7:45 am

15. What is the angle between the hour and minute hands of a clock at 11:40?

A) 130 degrees

B) 135 degrees

C) 140 degrees

D) 145 degrees

Answer: B) 135 degrees

16. If the time now is 9:55 pm, what will be the time 4 hours and 45 minutes later?

A) 2:40 am

B) 2:40 pm

C) 3:40 am

D) 3:40 pm

Answer: C) 3:40 am

17. What is the angle between the hour and minute hands of a clock at 5:15?

A) 27.5 degrees

B) 30 degrees

C) 32.5 degrees

D) 35 degrees

Answer: B) 30 degrees

18. If the time now is 12:20 pm, what will be the time 3 hours and 40 minutes later?

A) 3:00 pm

B) 3:00 am

C) 4:00 pm

D) 4:00 am

Answer: C) 4:00 pm

19. What is the angle between the hour and minute hands of a clock at 8:25?

A) 117.5 degrees

B) 122.5 degrees

C) 127.5 degrees

D) 132.5 degrees

Answer: B) 122.5 degrees

20. If the time now is 2:10 pm, what will be the time 5 hours and 20 minutes later?

A) 7:30 pm

B) 7:30 am

C) 8:30 pm

D) 8:30 am

Answer: A) 7:30 pm

These examples illustrate how to apply clock-related concepts to solve problems and answer questions related to time.

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