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1. Find at what time between 8 and 9 o’clock will the hands of a clock be in the same straight line but not together.
Explanation:
At 8 o’clock, the hour hand is at 8 and the minute hand is at 12, i.e. the two hands are 20 min. spaces apart.
To be i the same straight line but not together they will be 30 minute spaces apart. So, the minute hand will have to gain (30 - 20) = 10 minute spaces over the hour hand.
55 minute spaces are gained in 60 min.
10 minute spaces will be gained in [60/55 * 10] min. = 10 10/11 min.
=> The hands will be in the same straight line but not together at 10 10/11 min. past 8.
2. Find the angle between the hour hand and the minute hand of a clock when the time is 3.25.
Explanation:
Angle traced by the hour hand in 12 hours = 360°.
Angle traced by it in 3 hrs 25 min. i.e. 41/12 hrs =
[360 / 12 * 41/12] = 102½°
Angle traced by minute hand in 60 min. = 360°.
Angle traced by it in 25 min. = [360 / 60 * 25]° = 150°.
=> Required angle = [150° - 102½°] = 47½.
3. A watch which gains uniformly, is 5 min. slow at 8 o’clock in the morning on Sunday and it is 5 min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct?
Explanation:
Time from 8 a.m. on Sunday to 8 p.m. on following Sunday = 7 days 12 hours = 180 hours.
=> The watch gains [5+5 4/5] min. or 54/5 min. in 180 hrs.
Now 54/5 min. are gained in 180 hrs.
=> 5 min. are gained in [180 * 5/54 * 5] hrs. = 83 hrs 20 min. = 3 days 11 hrs 20 min.
=> It will be correct at 20 min. past 7 p.m. on Wednesday.
4. How many times are the hands of a clock at right angle in a day?
Explanation:
In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
5. How many times in a day, are the hands of a clock in straight line but opposite in direction?
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'clcok only).
So, in a day, the hands point in the opposite directions 22 times.
Explanation:
At 8 o’clock, the hour hand is at 8 and the minute hand is at 12, i.e. the two hands are 20 min. spaces apart.
To be i the same straight line but not together they will be 30 minute spaces apart. So, the minute hand will have to gain (30 - 20) = 10 minute spaces over the hour hand.
55 minute spaces are gained in 60 min.
10 minute spaces will be gained in [60/55 * 10] min. = 10 10/11 min.
=> The hands will be in the same straight line but not together at 10 10/11 min. past 8.
2. Find the angle between the hour hand and the minute hand of a clock when the time is 3.25.
Explanation:
Angle traced by the hour hand in 12 hours = 360°.
Angle traced by it in 3 hrs 25 min. i.e. 41/12 hrs =
[360 / 12 * 41/12] = 102½°
Angle traced by minute hand in 60 min. = 360°.
Angle traced by it in 25 min. = [360 / 60 * 25]° = 150°.
=> Required angle = [150° - 102½°] = 47½.
3. A watch which gains uniformly, is 5 min. slow at 8 o’clock in the morning on Sunday and it is 5 min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct?
Explanation:
Time from 8 a.m. on Sunday to 8 p.m. on following Sunday = 7 days 12 hours = 180 hours.
=> The watch gains [5+5 4/5] min. or 54/5 min. in 180 hrs.
Now 54/5 min. are gained in 180 hrs.
=> 5 min. are gained in [180 * 5/54 * 5] hrs. = 83 hrs 20 min. = 3 days 11 hrs 20 min.
=> It will be correct at 20 min. past 7 p.m. on Wednesday.
4. How many times are the hands of a clock at right angle in a day?
Explanation:
In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
5. How many times in a day, are the hands of a clock in straight line but opposite in direction?
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'clcok only).
So, in a day, the hands point in the opposite directions 22 times.
1 comments:
In question 3 please explain how do u get 54/5?
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