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- Question 1 of 24
##### 1. Question

In 16 minutes, the minute hand gains over the hour hand by:

##### Hint

The minute hand covers 6° in one minute and the hour hand covers 0.5° in one minute.

Thus, minute hand will gain (6–0.5)=5.5° over the hour hand in one minute.

In 16 minutes, the minute hand gains (16×5.5)=88° over the hour hand. - 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°

So, 3 minutes will make 6×3=18° - Question 3 of 24
##### 3. Question

What will be the angle between hands of a clock at 2:30?

##### Hint

The minute hand covers 6° in one minute and the hour hand covers 0.5° in one minute.

Thus, the minute hand will*gain*(6–0.5)=5.5° over the hour hand in one minute.At 2’o Clock, Minute Hand will be 10×6=60° behind the Hour Hand.

In 30 minutes, Minute Hand will gain 5.5°×30=165°.

The 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

The minute hand covers 6° in one minute and the hour hand covers 0.5° in one minute.

Thus, the minute hand will*gain*(6–0.5)=5.5° over the hour hand in one minute.

At 8:00 pm, the angle between Minute Hand and Hour Hand will be 40×6=240°.

In 24 minutes, Minute Hand will gain 24×5.5=132°.

Required angle =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

The minute hand covers 6° in one minute and the hour hand covers 0.5° in one minute.

Thus, the minute hand will*gain*(6–0.5)=5.5° over the hour hand in one minute.

At 5:00 pm, the angle between Minute Hand and Hour Hand will be 25×6=150°.

In 15 minutes, Minute Hand will gain 15×5.5=82.5°.

Required angle =150–82.5=67.5°. - 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

The minute hand covers 6° in one minute and the hour hand covers 0.5° in one minute.

Thus, the minute hand will*gain*(6–0.5)=5.5° over the hour hand in one minute.

At 3 o’clock, the angle between Minute Hand and Hour Hand will be 15×6=90°.

In 25 minutes, Minute Hand will gain 25×5.5=137.5°.

Required angle =137.5–90=47.5°. - 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

=33÷3=11 seconds each

Therefore, to strike 6 it has 5 equal intervals,

it requires 5×3=15 seconds - 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 minutes space apart.

At 7 o’clock, they are a 25 minutes space apart.

So, the minute hand will have to gain only 5 minutes space.Minute hand gains 55 minutes space in 60 minutes.

5 minutes space will gain in:

Required time =5^{5}⁄_{11}minutes past 7 - 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

At 4 o’clock, the hands are 20 minutes space apart.

To be at right angles and that too between 4 and 5, the minute hand has to gain (20+15) =35 minutes space.

Minute hand gains 55 minutes space in 60 minutes.

35 minutes space will gain in:

(60/55)×35=38.18

Required time =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 minutes space apart.

To be at right angles and that too between 5:30 and 6, the minute hand has to gain (25+15) =40 minutes space.

Minute hand gains 55 minutes space in 60 minutes.

40 minutes space will gain in:

Required time =43^{7}⁄_{11}minutes past 5 - 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 minutes space apart.

To be in opposite directions, they must be 30 minutes space apart.

So, the Minute hand will have to gain (20+30)= 50 minutes space.

Minute hand gains 55 minutes space in 60 minutes.

50 minutes space will gain in:

Required time=54^{6}⁄_{11}minutes past 4 - 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 hands of the watch are 15 minutes space apart.

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 (30–15)= 15 minutes space over Hour Hand.

Minute hand gains 55 minutes space in 60 minutes.

15 minutes space will gain in:

(60/55)×15 = 16^{4}⁄_{11}

Required time= 16^{4}⁄_{11}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

At 3 o’clock, the hands of the watch are 15 minutes space apart.

The hands will coincide with each other when there is a space of 0 minutes between them.

This will happen when the Minute Hand gains (15–0)=15 minutes space over Hour Hand.

Minute hand gains 55 minutes space in 60 minutes.

15 minutes space will gain in:

(60/55)×15 = 16^{4}⁄_{11}

Required time= 16^{4}⁄_{11}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

At 7 o’clock, the hands of the watch are 35 minutes space apart.

The hands will coincide with each other when there is a space of 0 minutes between them.

This will happen when the Minute Hand gains (35–0)=35 minutes space over Hour Hand.

Minute hand gains 55 minutes space in 60 minutes.

35 minutes space will gain in:

(60/55)×35 = 38.18

Required time= 38.18 minutes past 7 - Question 15 of 24
##### 15. Question

How much does a watch lose per day, if its hands coincide every 64 minutes?

##### Hint

The minute hand of the accurate watch gains 55 minutes space in 60 minutes.

60 minutes space will cover in

Loss in 64 minutes

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

Number of hours between 8 o’clock in the morning and 2 o’clock in the afternoon is 6.

Angle traced by the hour hand in 6 hours

- Question 17 of 24
##### 17. Question

A clock is set right at 5 am The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 pm on the 4th day?

##### Hint

Time from 5 am on a day to 10 pm on the 4th day is 89 hours.

Now, 23 hours 44 minutes of this clock are the same as 24 hours of the correct clock.

i.e., ³⁵⁶⁄₁₅ hours of this clock are the same as 24 hours of the correct clock.

Thus, 89 hours of this clock are the same as:hours of the correct clock.

= 90 hrs of the correct clock.

So, the correct time is 11 pm. - Question 18 of 24
##### 18. Question

A watch which gains 5 seconds in 3 minutes was set right at 7 am. In the afternoon of the same day, when the watch indicated quarter past 4 o’clock, the true time is:

##### Hint

Time from 7 am to quarter past 4

= 9 hours 15 minutes = 555 minutes

Now, (3 min +5 sec) = 37⁄12 minutes of this watch are the same as 3 minutes of the correct watch.

555 minutes of this watch will be the same as:

minutes of the correct watch.

= 9 hours of the correct watch.

The correct time is 9 hours after 7 am i.e., 4 pm - 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

Time from 12 noon to 4.00 am, the next day

= 16 hours

The clock gains 15 minutes 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 pm. If it gains one minute in an hour, then what is the true time when the clock indicates 6 pm in the same day?

##### Hint

Time interval indicated by the incorrect clock from 1 pm to 6 pm

= 5 hours = 300 minutes

Now, 61 minutes of this watch are the same as 60 minutes of the correct watch.

300 minutes of this watch will be the same as:

(60/61)×300 minutes of the correct watch.

= 4^{56}⁄_{61}hours of the correct watch.

The correct time is 4^{56}⁄_{61}hours after 1 pm

Thus, the true-time = 55^{5}⁄_{61}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 is 75 hours.

24 hours 2 minutes of the first clock are the same as 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 the correct one.

= 54000/721 hours = 74 hours 53.7 minutes.

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 hr 18 min 15 sec of watch time. What is the time gained or lost by this watch in one day?

##### Hint

Minute hand gains 55 minutes space in 60 minutes.

In a watch that is running correctly, the minute hand should cross the hour hand once in every:

60×(60/55) minutes.

So they should ideally cross 3 times once in:

3×60×(60/55) minutes =196.36 minutes.But in the watch under consideration, they meet after every 3hr, 18 min and 15 seconds, i.e. 198.25 minutes.

Thus, the watch is actually losing time (as it is slower than the normal watch).Hence 1 day (1440 min) of this watch will be:

1440×(196.36/198.25) = 1426.27 minutes.Hence the amount of time lost the watch in one day:

=1440–1426.27=13.73 minutes

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 am on Monday. What will be the true time when the clock indicates 10:30 am on the next Sunday?

##### Hint

Time between 10 am on Monday to 10:30 am on Sunday

= 6 days and ½ hrs = 144.5 hrs.24 hr + 5 min = 289/12 hours of incorrect clock = 24 hours of correct time.

So, 144.5 hours of the incorrect clock

= 144.5×24/(289/12) hours of the correct time

= 144 hours i.e., the true time is 10 am 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 pm on the following Monday. When was it correct?

##### Hint

Time from 12 pm on Monday to 2 pm on the following Monday

= 7 days 2 hours = 170 hours.The watch gains

Now, 34/5 minutes are gained in 170 hrs.

So, 2 minutes are gained in

Watch is correct 2 days 2 hrs. after 12 pm on Monday i.e., it will be correct at 2 pm on Wednesday.