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Question 1 of 24
1. Question
In 16 minutes, the minute hand gains over the hour hand by
Hint
In 1 hour, the minute hand gains 330° over the hour hand. i.e. in 60 minute, the minute hand gains 330° over the hour hand.
∴ In 16 minutes, the minute hand gains over the hour hand by 
Question 2 of 24
2. Question
If the two hands in a clock are 3 minutes divisions apart, then the angle between them is
Hint
In a clock, each minute makes 6°
∴ 3 minutes will make 6 × 3 = 18° 
Question 3 of 24
3. Question
What will be the acute angle between hands of a clock at 2 : 30?
Hint
At 2’O Clock, Minute Hand will be 10 × 6 = 60° behind the Hour Hand.
In 30 minutes, Minute Hand will gain 5 ½° × 30 = 150 + 15 = 165°
∴Angle between Hour Hand and Minute Hand = 165 – 60 = 105° 
Question 4 of 24
4. Question
What is the angle between the 2 hands of the clock at 8:24 pm?
Hint
Required angle = 240 – 24 × (11/2) = 240 –132 = 108°.

Question 5 of 24
5. Question
At what angle the hands of a clock are inclined at 15 minutes past 5 ?
Hint
At 15 minutes past 5, the minute hand is at 3 and hour hand slightly advanced from 5. Angle between their 3rd and 5th position.
Angle through which hour hand shifts in 15 minutes is
∴Required angle = 
Question 6 of 24
6. Question
Find the angle between the hour hand and the minute hand of a clock when the time is 3.25.
Hint
Angle traced by the hour hand in 12 hours = 360°
Angle traced by it in 3 hrs 25 min. i.e.
Angle traced by it in 25 min.
Required angle 
Question 7 of 24
7. Question
If a clock strikes 12 in 33 seconds, it will strike 6 in how many seconds?
Hint
In order to strike 12, there are 11 intervals of equal time
Therefore, to strike 6 it has 5 equal intervals, it requires 5 × 3 = 15 sec. 
Question 8 of 24
8. Question
At what time between 7 and 8 o’clock will the hands of a clock be in the same straight line but, not together?
Hint
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o’clock, they are 25 min. spaces apart.
∴ Minute hand will have to gain only 5 in. spaces.
55 min. spaces are gained in 60 min.
5 min. spaecs are gained in

Question 9 of 24
9. Question
At what approximate time between 4 and 5 am will the hands of a clock be at right angle?
Hint
Here H × 30 = 4 × 30 = 120°.
(Since initially the hour hand is at 4.∴ H = 4).
Required angle A = 90° and since, H × 30 > A° so, there will be two timings.
Required time T = ²⁄₁₁ (H × 30 ± A) minutes past H.
∴ One timing = ²⁄₁₁ (4 × 30 + 90) minutes past 4.
= 38 ²⁄₁₁ minutes past 4.
Or 4 : 38 approx. 
Question 10 of 24
10. Question
At what time between 5.30 and 6 will the hands of a clock be at right angles?
Hint
At 5 o’clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces
55 min. spaces are gained in 60 min.
40 min. spaces are gained in

Question 11 of 24
11. Question
At what time between 4 and 5 o’clock will the hands of a watch point in opposite directions?
Hint
At 4 o’clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
∴ Minute hand will have to gain 50 min. spaces
55 min. spaces are gained in 60 min.
50 min. spaces are gained in

Question 12 of 24
12. Question
At what time between 9’o clock and 10’o clock will the hands of a clock point in the opposite directions?
Hint
At 9’o clock, the Minute Hand is ahead of Hour Hand by 15 minutes. The hands will be opposite to each other when there is a space of 30 minutes between them.
This will happen when the Minute Hand gains 15 minutes’ space over Hour Hand.
Time taken by Minutes Hand to gain 15 minutes
Hence the Hands are opposite to each other at minutes past 9. 
Question 13 of 24
13. Question
At what time between 3 and 4 o’clock, the hands of a clock coincide?
Hint
Since, in one hour, two hands of a clock coincide only once, so, there will be value.
Required time T = minutes past H.
Here H = initial position of hour hand = 3(Since 3 o’clock)
A° = required angle = 0°(Since it coincides)
T = minutes past 3 = minutes past 3. 
Question 14 of 24
14. Question
Find the exact time between 7 am and 8 am when the two hands of a watch meet ?
Hint
55 min spaces are gained in 60 min
⇒35 min spaces will be gained in 38.18 min.
⇒Answer = 7 hrs + 38.18 min. 
Question 15 of 24
15. Question
How much does a watch lose per day, if its hands coincide every 64 minutes?
Hint
55 min. spaces are covered in 60 min.
60 min. spaces are covered in
Loss in 64 min.
Loss in 24 hrs. 
Question 16 of 24
16. Question
An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?
Hint
Angle traced by the hour hand in 6 hours

Question 17 of 24
17. Question
A clock is set right at 5 a.m. The clock loses 16 min. in 24 hours. What will be the true time when the clock indicates 10 p.m. on the 4th day ?
Hint
Time from 5 a.m. on a day to 10 p.m. on 4th day is 89 hours.
Now, 23 hrs. 44 min. of this clock are the same as 24 hours of the correct clock.
i.e., ³⁵⁶⁄₁₅ hrs. of this clock = 24 hrs. of correct clock.
∴89 hrs. of this clock =hrs. of correct clock
= 90 hrs of correct clock.
So, the correct time is 11 p.m. 
Question 18 of 24
18. Question
A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 O’clock, the true time is:
Hint
Time from 7 a.m. to quarter pas 4
= 9 hours 15 min.=555 min.
Now, 37⁄12 min. of this watch = 3 min. of the correct watch.
555 min. of this watch = min.
= of the correct watch.
Correct time is 9 hours after 7 a.m. i.e., 4 p.m. 
Question 19 of 24
19. Question
A clock gains 15 minutes per day. It is set right at 12 noon. What time will it show at 4.00 am, the next day?
Hint
The clock gains 15 min in 24 hours.
Therefore, in 16 hours, it will gain 10 minutes.
Hence, the time shown by the clock will be 4.10 am. 
Question 20 of 24
20. Question
A clock is set right at 1 p.m. If it gains one minute in an hour, then what is the true time when the clock indicates 6 p.m. in the same day?
Hint
Time interval indicated by incorrect clock = 6 p.m – 1 p.m = 5 hrs.
Time gained by incorrect clock in one hour = + 1 min.= + 1/60 hr.
Using the formula,
⇒ True time interval
∴ True time = 1 p.m. + hrs. = 5 p.m. + hrs.
= 5 p.m. + × 60 min = minutes past 5. 
Question 21 of 24
21. Question
Two clocks were set right at noon on Sunday. One gains 2 min and the other loses 3 min in 24 hours. What will be the true time when the first clock indicates 3 pm on Wednesday?
Hint
Time from noon on Sunday to 3 pm on Wednesday = 75 hours.
24 hours 2 minutes of the first clock= 24 hours of the correct one.
⇒ 1 hour of the first clock= 24 × (30/721) hours of correct one.
⇒ 75 hours of the first clock = 24 × 30 × (75/721) hours of correct one
= 54000/721 hours = 74 hours 53.7 min.
Hence the answer is 2:54 pm. 
Question 22 of 24
22. Question
In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hrs. 18 min. 15 seconds of watch time. What is the time gained or lost by this watch in one day?
Hint
In a watch than is running correct the minute hand should cross the hour hand once in every min. So they should ideally cross 3 times once in min = 196.36 minutes.
But in the watch under consideration, they meet after every 3hr, 18 min and 15 seconds,
i.e. min.
Thus, our watch is actually losing time (as it is slower than the normal watch). Hence when our watch elapsed = 1426.27.
Hence the amount of time lost by our watch in one day i.e., 13 min and 50s (approx). 
Question 23 of 24
23. Question
A clock gains 5 minutes. in 24 hours. It was set right at 10 a.m. on Monday. What will be the true time when the clock indicates 10:30 a.m. on the next Sunday ?
Hint
Time between 10 a.m. on Mon to 10:30 a.m. on Sun = 144 ½ hrs.
24 ½ hours of incorrect clock = 24 hours of correct time.
∴144 ½ hours of incorrect clock = x hours of correct time.
∴x = = 144 hours i.e., the true time is 10 a.m. on Sunday. 
Question 24 of 24
24. Question
A watch which gains uniformly is 2 minutes slow at noon on Monday and is 4 min. 48 sec. fast at 2 p.m. on the following Monday. When was it correct?
Hint
Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.
∴ The watch gains
Now, min. are gained in 170 hrs.
∴ 2 min. are gained in
∴ Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e. it will be correct at 2 p.m. on Wednesday.