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At what time between 5 and 6 o’ clock are the hands of a 3 minutes apart ?

A.

14min

B.

24min

C.

20min

D.

12min

Answer with explanation

Answer: Option BExplanation

In this type of problems the formulae is

(5*x+ or – t)*12/11

Here x is replaced by the first interval of given time. Here x is 5.

t is spaces apart

**Case 1 :** (5*x + t) * 12/11

(5*5 + 3) * 12/11

28 * 12/11 = 336/11= 31 5/11 min

therefore the hands will be 3 min apart at 31 5/11 min past 5.

**Case 2** : (5*x – t) * 12/11

(5*5 -3 ) * 12/11

22 *12/11 = 24 min

therefore the hands will be 3 min apart at 24 min past 5

Workspace

Find the angle between the hour hand and the minute hand of a clock when the time is 3.25

A.

46.5°

B.

48.5°

C.

47.5°

D.

45.5°

Answer with explanation

Answer: Option CExplanation

At 3 O’clock, Minute hand is at 12 while the Hour hand is at 3. Again the minute hand has to sweep through ( 30 x 5 ) ie 150° for reaching the figure 5 to show 25 mins.

Simultaneously the Hour hand will also rotate for 25 mins. Thus starting from the mark, 3 the hour hand will cover an angle = (25 x 30) / 60 = 12.5°

Hence, Angle between Hour and the Minute hand = ( 60 – 12.5 ) = 47.5°

Workspace

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 ?

A.

8 p.m.

B.

9 p.m.

C.

10 p.m.

D.

11 p.m.

Answer with explanation

Answer: Option DExplanation

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.

Workspace

**A clock strikes 4 taking 9 seconds. In order to strike 12 at the same rate, the time taken is**

A.

28 seconds

B.

30 seconds

C.

36 seconds

D.

33 seconds

Answer with explanation

Answer: Option DExplanation

There are 3 intervals when the clock strikes 4

Time taken for 3 intervals = 9 seconds

Time taken for 1 interval = 9/3=3 seconds

In order to strike 12, there are 11 intervals.

Hence time needed =3×11=33 seconds

Workspace

At what time between 9 &10 will the hands of a watch be together?

A.

48 min past 9

B.

47 min past 9

C.

49 1/11 min past 9

D.

45 min past 9

Answer with explanation

Answer: Option CExplanation

To be together between 9 and 10 O’clock, the minute hand has to gain 45min.

spaces 55min. spaces are gained in 60min.

45min.spaces are gained in (60/55 × 45) min. or 49 1/11 min.

The hands are together at 49 1/11 min. past 9.

Workspace

If the minute hand of a clock has moved 300º, how many degrees has the hour hand moved?

A.

300°

B.

50°

C.

25°

D.

150°

Answer with explanation

Answer: Option CExplanation

The speed of hour hand is 0.5 dpm (Degree per Minute)

And the speed of minute hand is 6 dpm.

So, 300 degree traverse by minute hand in 300/6 = 50 Minutes.

Thus, angle moved by the hour hand in 50 minutes is 50/0.5 = 25° degrees.

Workspace

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much the clock gain or lose in a day?

A.

10(54/42) min

B.

10(10/43) min

C.

10(53/41) min

D.

10(12/46) min

Answer with explanation

Answer: Option BExplanation

In a correct clock, the minute hand gains 55 min. spaces over

the hour hand in 60 min.

55 min. are gained in 60 min.

60 min. are gained in (60/55) X 60=65(5/11) min

But, they are together after 65 min.

Therefore, Gain in 65 min=(65(5/11)-65) =5/11.

Gain in 24 hours = (5/11) X ((60 X 24)/65)=10(10/43) min.

Therefore, *The clock gains 10(10/43) min. in a day.*

Workspace

A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?

A.

2 p.m. on Wednesday

B.

3 p.m. on Wednesday

C.

2 p.m. on Thursday

D.

3 p.m. on Thursday

Answer with explanation

Answer: Option AExplanation

**Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.**

**∴ 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.**

Workspace

How many times do the hands of a clock coincide in a day?

A.

22

B.

24

C.

21

D.

20

Answer with explanation

Answer: Option AExplanation

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, *i.e.,* at 12 o’clock).

**AM**

12:00

1:05

2:11

3:16

4:22

5:27

6:33

7:38

8:44

9:49

10:55

**PM**

12:00

1:05

2:11

3:16

4:22

5:27

6:33

7:38

8:44

9:49

10:55

The hands overlap about every 65 minutes, not every 60 minutes.

The hands coincide 22 times in a day.

Workspace

An accurate clock shows 8 o’clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?

A.

60

B.

90

C.

180

D.

360

Answer with explanation

Answer: Option CExplanation

Angle traced by the hour hand in 6 hours=(360/12)*6

Workspace

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

A.

88°

B.

80°

C.

60°

D.

90°

Answer with explanation

Answer: Option AExplanation

In 1 hour, the minute hand gains 330° over the hour hand. i.e. in 60 minutes, the minute hand gains 330° over the hour hand.

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

Workspace

How many times in a day, are the hands of a clock in straight line but opposite in direction?

A.

12

B.

22

C.

24

D.

48

Answer with explanation

Answer: Option BExplanation

The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 ‘o clock only.

Hence the hands point in the opposite directions 22 times in a day.

This is already given as a formula and it’s is better to learn the answer by heart as 22 which can save time in competitive exams. (However, you should know the theory behind).

Workspace

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

A.

96min

B.

90min

C.

36 5/11min

D.

32 8/11min

Answer with explanation

Answer: Option DExplanation

55 min. spaces are covered in 60 min.

60 min spaces are covered in (60/55 × 60)min = 65 5/11 min

Loss in 64 min = ( 65 5/11- 64 ) = 16/11 min

Loss in 24 hrs = ( 16/11 × 1/64 × 24 × 60 ) min

= 32 8/11 min

Workspace

A watch gain 8 seconds in 4 minutes and was set right at 4 AM. What time will it show at 11 PM on the same day?

A.

11:38

B.

12:08

C.

11:08

D.

12:38

Answer with explanation

Answer: Option AExplanation

8 Seconds in 4 Minutes mean 120 Seconds (or 2 Minutes) in one hour.

From 4AM to 11PM (on the same day) = 19 hours

So, total seconds gain in 19 hours = 19 X 120 (Seconds gain per hour) = 2280 Seconds.

Now, 2280 Seconds = 38 Minutes (i.e. 2280/19 = 38)

Thus incorrect clock will show 11:38PM at 11PM.

Workspace

A clock which loses uniformly was observed to be 5 minutes fast at 4:00 p.m on a Friday. On the subsequent Sunday at 8:00 a.m, the watch was 3 minutes slow. When did the watch show the correct time?

A.

8:00 p.m. on Saturday

B.

5:00 p.m. on Saturday

C.

4:00 p.m. on Saturday

D.

7:00 p.m. on Saturday

Answer with explanation

Answer: Option BExplanation

Number of minutes lost = 8

Total time from 4:00 p.m. on Friday to 8:00 a.m. on

Sunday = 40 hours.

There for, It lost 8 minutes in 40 hours

Time taken to lose 5 minutes = ( 40 x 5) / 8= 25 hours.

Whenever it lost the first 5 minutes, the clock is going to show the correct time.

After 25 hours (i.e.,) at **5:00 p.m. on Saturday** the cock shows the correct time

Workspace

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