1️⃣ How many degrees does the hour hand move in one hour?
Step-by-Step Explanation
The hour hand completes 360° in 12 hours.
Therefore, in 1 hour, it moves 360° / 12 = 30°.
Answer: 30° ✅
2️⃣ How many degrees does the minute hand move in one minute?
Step-by-Step Explanation
The minute hand completes 360° in 60 minutes.
Therefore, in 1 minute, it moves 360° / 60 = 6°.
Answer: 6° ✅
3️⃣ What is the angle between the hour and minute hand at 3:00?
Step-by-Step Explanation
At 3:00, the hour hand is at 3 and the minute hand is at 12.
There are 3 intervals between them, and each interval is 30°.
Therefore, the angle is 3 * 30° = 90°.
Answer: 90° ✅
4️⃣ At what time between 4 and 5 o'clock will the hands of a clock coincide?
Step-by-Step Explanation
Let the minutes past 4 be 'x'.
At 4 o'clock, the hour hand is at 120° (4 * 30°) and the minute hand is at 0°.
The hour hand moves 0.5° per minute, and the minute hand moves 6° per minute.
For the hands to coincide, 120 + 0.5x = 6x.
120 = 5.5x.
x = 120 / 5.5 = 240 / 11 = 21 9/11 minutes.
Therefore, the time is 4:21 9/11.
Answer: 4:21 9/11 ✅
5️⃣ What is the angle between the hour and minute hand at 7:30?
Step-by-Step Explanation
At 7:00, the angle is 7 * 30° = 210°.
In 30 minutes, the hour hand moves 30 * 0.5° = 15°.
In 30 minutes, the minute hand moves 30 * 6° = 180°.
The hour hand is at 210° + 15° = 225°.
The minute hand is at 180°.
The difference is 225° - 180° = 45°.
Answer: 45° ✅
6️⃣ How many times do the hands of a clock coincide in 12 hours?
Step-by-Step Explanation
The hands coincide 11 times in 12 hours (they coincide once between every hour except between 11 and 1).
Answer: 11 ✅
7️⃣ A clock gains 5 minutes in an hour. How much will it gain in 24 hours?
Step-by-Step Explanation
The clock gains 5 minutes per hour.
In 24 hours, it will gain 5 * 24 = 120 minutes.
120 minutes = 120 / 60 = 2 hours.
Answer: 2 hours ✅
8️⃣ A clock gains 10 minutes in 24 hours. What is the actual time when the clock shows 1 PM on the following day, if it was set right at 8 AM?
Step-by-Step Explanation
The clock gains 10 minutes in 24 hours.
From 8 AM to 1 PM the next day, there are 29 hours.
Gain in 29 hours = (10/24) * 29 = 290/24 = 12 2/24 = 12 1/12 minutes.
12 1/12 minutes = 12 minutes and 5 seconds.
The clock shows 1 PM, which means the actual time is 12 minutes and 5 seconds earlier.
1 PM - 12 minutes 5 seconds = 12:47:55 PM, which is roughly 12:48 PM.
Answer: 12:48 PM ✅
9️⃣ At what time between 9 and 10 o'clock will the hands of a clock be in opposite directions?
Step-by-Step Explanation
At 9 o'clock, the hour hand is at 270° (9 * 30°) and the minute hand is at 0°.
For the hands to be in opposite directions, the angle between them should be 180°.
Let 'x' be the minutes past 9.
270 + 0.5x - 6x = 180 or 6x - 270 - 0.5x = 180.
90 = 5.5x or 5.5x = 450.
x = 90/5.5 = 180/11 = 16 4/11 minutes.
Answer: 9:16 4/11 ✅
🔟 A faulty clock gains 16 minutes in 24 hours. It was set right at 9 AM on a Monday. When the clock shows 11 PM on the following Thursday, what is the correct time?
Step-by-Step Explanation
From 9 AM Monday to 11 PM Thursday, there are 74 hours.
Gain in 74 hours = (16/24) * 74 = (2/3) * 74 = 148/3 = 49 1/3 minutes.
49 1/3 minutes = 49 minutes and 20 seconds.
The clock shows 11 PM, which means the actual time is 49 minutes and 20 seconds earlier.
11 PM - 49 minutes 20 seconds = 10:10:40 PM, which is roughly 10:11.