Clock Aptitude Formula, Clock Problem Shortcuts and Tricks

Clock Important Questions - Page 2
Clock Video Lecture - Page 3

Clock: The Face or dial of a watch is a circle whose circumference is divided into 60 equal parts, called minute spaces. A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.

Clock Important Formulas

In 60 minutes, the minute hand gains 55 minutes on the hour hand
In every hour, both the hands coincide once.
The hands are in the same straight line when they are coincident or opposite to each other.
When the two hands are at right angles, they are 15 minute spaces apart
When the hand's are in opposite directions, they are 30 minute spaces apart
Angle traced by hour hand in 12 hrs = 360°.
Angle traced by minute hand in 60 min. = 360°.
Too Fast and Too Slow: If a watch or a clock indicates 8.15, when the correct time , 8 is said to be 15 minutes too fast.
On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.

Solved Examples for Clock Problem

Question - 1: The angle between the minute hand and the hour hand of a clock when the time is 4 : 20

Solution: Angle traced by hour hand in

Angle traced by min. hand in 20 min. =

Required angle = (130 - 120)º = 10º.

Question - 2: How many times are the hands of a clock at right angle in a day?
Solution: In 12 hours, they are at right angles 22 times.

In 24 hours, they are at right angles 44 times.

Question -3: How many times in a day, are the hands of a clock in straight line but opposite in direction?

Solution: 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

Question - 4: At what time between 9 and 10 o'clock will the hands of a watch be together?
Solution: To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces. 55 min. spaces gained in 60 min.

45 min. spaces are gained in min

The hands are together at min past 9

Important Questions from Previous Year Paper

clock - Aptitude

Question 1 of 20

1. Question
1 points
At what angle the hands of a clock are inclined at 15 minutes past 5 ?
Correct

Angle traced by hour hand in

Angle traced by min. hand in 15 min.

Required angle

Incorrect

Angle traced by hour hand in

Angle traced by min. hand in 15 min.

Required angle
Question 2 of 20

2. Question
1 points
At what line,in minutes,between 3 o'clock and 4 o'clock,both the needles will coincide each other ? (R.R.B.2002)
Correct

At 3 o"clock ,the minute hand is 15 min.spaces apart from the hour hand.To be coincident,it must gain 15 min.spaces. 55 min.are gained in 60 min.

15 min.are gained in

The hands are coincident at min.past 3.

Incorrect

At 3 o"clock ,the minute hand is 15 min.spaces apart from the hour hand.To be coincident,it must gain 15 min.spaces. 55 min.are gained in 60 min.

15 min.are gained in

The hands are coincident at min.past 3.
Question 3 of 20

3. Question
1 points
At what times between 9 and 10 o"clock will the hands of a watch be together ?
- 25 min. past 9
- 20 min. past 9
Correct

To be together between 9 and 10 o"clock,the minute hand has to gain 45 min.spaces.55 min.spaces gained in 60 min.
45 min.spaces are gained in .or
$\therefore$ The hands are together at min past 9

Incorrect

To be together between 9 and 10 o"clock,the minute hand has to gain 45 min.spaces.55 min.spaces gained in 60 min.
45 min.spaces are gained in .or
$\therefore$ The hands are together at min past 9
Question 4 of 20

4. Question
1 points
At what time between 7 and 8 o"clock will the hands of a clock be in the same straight line but,not together ? (A.A.O.exam.2003)
- 5 min.past 7
- min.past 7
- min.past 7
- min.past 7
Correct

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 min. spaces.

55 min.spaces are gained in

Required time = min.past 7

Incorrect

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 min. spaces.

55 min.spaces are gained in

Required time = min.past 7
Question 5 of 20

5. Question
1 points
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 Monday.When was it correct ?(R.R.B.2001)
- 1 p.m. on Tuesday
- 2 p.m. on Wednesday
- 4 p.m. on Thursday
- 1 p.m. on Friday
Correct

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

The watch gain min . or min.in 170hrs

Now, min.are gained in 170hrs.

2 min. are gained in hrs=50hrs.

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.

Incorrect

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

The watch gain min . or min.in 170hrs

Now, min.are gained in 170hrs.

2 min. are gained in hrs=50hrs.

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.
Question 6 of 20

6. Question
1 points
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 :
- min. past 3
- 4 p.m.
- min.past 3
- min.past 3
Correct

Time from 7 a.m. to 4.15 p.m. =9 hrs 15 min.= hrs.

3 min. 5 sec. of this clock = 3 min. of the correct clock

hrs of this clock = hrs of the correct clock

hrs of this clock hrs of the correct clock

The correct time is 9 hrs after 7 a.m i.e 4 p.m

Incorrect

Time from 7 a.m. to 4.15 p.m. =9 hrs 15 min.= hrs.

3 min. 5 sec. of this clock = 3 min. of the correct clock

hrs of this clock = hrs of the correct clock

hrs of this clock hrs of the correct clock

The correct time is 9 hrs after 7 a.m i.e 4 p.m
Question 7 of 20

7. Question
1 points
The angle between the minute hand and the hour hand of a clock when the time is 8.30, is
- 70 $^{\circ}$
- 75 $^{\circ}$
- 65 $^{\circ}$
- 145 $^{\circ}$
Correct

Angle traced by hour hand in $\frac{17}{2}hrs =(\frac{360}{12}\times \frac{17}{2})^{\circ} = 255.$

Angle traced by min. hand in 30 min. = $(\frac{360}{60}\times 30)^{\circ}$ = 180.

$\therefore$ Required angel = $(255-180^{\circ})=75^{\circ}$

Incorrect

Angle traced by hour hand in $\frac{17}{2}hrs =(\frac{360}{12}\times \frac{17}{2})^{\circ} = 255.$

Angle traced by min. hand in 30 min. = $(\frac{360}{60}\times 30)^{\circ}$ = 180.

$\therefore$ Required angel = $(255-180^{\circ})=75^{\circ}$
Question 8 of 20

8. Question
1 points
The angle between the minute hand and the hour hand of a clock when the time is 4.20 is :
- 0 $^{\circ}$
- 10 $^{\circ}$
- 3 $^{\circ}$
- 30 $^{\circ}$
Correct

Angle traced by hour hand in $\frac{13}{3}hrs = (\frac{360}{12}\times \frac{13}{3})^{\circ} = 130^{\circ}$

Angle traced by min. hand in 20 min.= $(\frac{360}{12}\times20^{\circ}) = 120^{\circ}$

$\therefore$ Required angle = $(130-120)^{\circ}=10^{\circ}$

Incorrect

Angle traced by hour hand in $\frac{13}{3}hrs = (\frac{360}{12}\times \frac{13}{3})^{\circ} = 130^{\circ}$

Angle traced by min. hand in 20 min.= $(\frac{360}{12}\times20^{\circ}) = 120^{\circ}$

$\therefore$ Required angle = $(130-120)^{\circ}=10^{\circ}$
Question 9 of 20

9. Question
1 points
An accurate clock shows 6 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 4 o'clock in the afternoon?
- $30^{\circ}$
- $60^{\circ}$
- $120^{\circ}$
- none of these
Correct

Angle traced by the hour hand in 2 hours = $(\frac{360}{12}\times 2)^{\circ}=60^{\circ}$

Incorrect

Angle traced by the hour hand in 2 hours = $(\frac{360}{12}\times 2)^{\circ}=60^{\circ}$
Question 10 of 20

10. Question
1 points
The reflex angle between the hands of a clock at 10.25 :
- $180^{\circ}$
- $192\frac{1}{2}^{\circ}$
- $195^{\circ}$
- $197\frac{1}{2}^{\circ}$
Correct

Angle traced by hour hand in $\frac{125}{12}hrs=(\frac{360}{12}\times \frac{125}{12})^{\circ}=312\frac{1}{2}^{\circ}$

Angle traced by minute hand in 25 min

$(\frac{360}{60}\times 25^{\circ})=150^{\circ}$
$\therefore Reflex angle=360^{\circ}-(312\frac{1}{2}-150)^{\circ}=360^{\circ}-162\frac{1}{2}^{\circ}=197\frac{1}{2}^{\circ}$

Incorrect

Angle traced by hour hand in $\frac{125}{12}hrs=(\frac{360}{12}\times \frac{125}{12})^{\circ}=312\frac{1}{2}^{\circ}$

Angle traced by minute hand in 25 min

$(\frac{360}{60}\times 25^{\circ})=150^{\circ}$
$\therefore Reflex angle=360^{\circ}-(312\frac{1}{2}-150)^{\circ}=360^{\circ}-162\frac{1}{2}^{\circ}=197\frac{1}{2}^{\circ}$
Question 11 of 20

11. Question
1 points
How many times do the hands of a clock at right angle in a day ? (I.A.S.1997)
- 25
- 42
- 44
- 82
Correct

In 12 hours, they are at right angles 22 times

$\therefore$ In 24 hours,they are at right angles 44 times.

Incorrect

In 12 hours, they are at right angles 22 times

$\therefore$ In 24 hours,they are at right angles 44 times.
Question 12 of 20

12. Question
1 points
How many times in a day, are the hands of a clock in straight line but opposite in direction ? (R.R.B.2003)
- 10
- 22
- 33
- 47
Correct

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'clock only).So, in a day, the hands point in the opposite directions 22 times.

Incorrect

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'clock only).So, in a day, the hands point in the opposite directions 22 times.
Question 13 of 20

13. Question
1 points
How much does a watch lose per day, if its hands coincide every 64 minutes ?
- $32\frac{8}{11}$ min
- $25\frac{5}{11}$ min
- 96 min
- 78 min
Correct

55 min. spaces are covered in 60 min.

60 min.spaces are covered in $(\frac{60}{55}\times 60)min.=65\frac{5}{11}min/$

Loss in 64 min.= $(65\frac{5}{11}-64)=\frac{16}{11}min.$

Loss in 24 hrs= $(\frac{16}{11}\times \frac{1}{64}\times 24\times 60)min=32\frac{8}{11}min.$

Incorrect

55 min. spaces are covered in 60 min.

60 min.spaces are covered in $(\frac{60}{55}\times 60)min.=65\frac{5}{11}min/$

Loss in 64 min.= $(65\frac{5}{11}-64)=\frac{16}{11}min.$

Loss in 24 hrs= $(\frac{16}{11}\times \frac{1}{64}\times 24\times 60)min=32\frac{8}{11}min.$
Question 14 of 20

14. Question
1 points
At what time between 4 and 5 o" clock will the hands of a watch point in opposite directions ?
- 35 min.past 4
- 20 min.past 4
- $50\frac{4}{11}$
- $54\frac{6}{11}$
Correct

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.

$\therefore$ Minute hand will have to gain 50 min.spaces.

55 min.spaces are gained in 60 min.

50 min.spaces are gained in $(\frac{60}{55}\times 50)min. or 54\frac{6}{11} min$

$\therefore$ Required time = $54\frac{6}{11}$ min.past 4

Incorrect

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.

$\therefore$ Minute hand will have to gain 50 min.spaces.

55 min.spaces are gained in 60 min.

50 min.spaces are gained in $(\frac{60}{55}\times 50)min. or 54\frac{6}{11} min$

$\therefore$ Required time = $54\frac{6}{11}$ min.past 4
Question 15 of 20

15. Question
1 points
At what time between 5.30 and 6 will the hands of a clock be at right angles ?
- $33\frac{5}{11} min. past 5$
- $43\frac{7}{11} min. past 5$
- 20 min . past 5
- 35 min. past 5
Correct

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 $(\frac{60}{55}\times 40) min =43\frac{7}{11} min.$

$\therefore$ Required time= $43\frac{7}{11} min. past 5$

Incorrect

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 $(\frac{60}{55}\times 40) min =43\frac{7}{11} min.$

$\therefore$ Required time= $43\frac{7}{11} min. past 5$
Question 16 of 20

16. Question
1 points
A clock is started at noon.by 10 minutes past 5,the hour hand has turned through:
- 135 $^{\circ}$
- 140 $^{\circ}$
- 155 $^{\circ}$
- 165 $^{\circ}$
Correct

Angle traced by hour hand in 12 hrs = 360 $^{\circ}$
Angle traced by hour hand in 5 hrs 10 min.i.e. $\frac{31}{6}hrs = (\frac{360}{12}\times \frac{31}{6})^{\circ}= 155^{\circ}$

Incorrect

Angle traced by hour hand in 12 hrs = 360 $^{\circ}$
Angle traced by hour hand in 5 hrs 10 min.i.e. $\frac{31}{6}hrs = (\frac{360}{12}\times \frac{31}{6})^{\circ}= 155^{\circ}$
Question 17 of 20

17. Question
1 points
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 ? (I.A.S.2000)
- 124 $^{\circ}$
- 150 $^{\circ}$
- 148 $^{\circ}$
- 180 $^{\circ}$
Correct

Angle traced by hour hand in 6 hours = $(\frac{360}{12}\times 6)^{\circ} = 180^{\circ}$

Incorrect

Angle traced by hour hand in 6 hours = $(\frac{360}{12}\times 6)^{\circ} = 180^{\circ}$
Question 18 of 20

18. Question
1 points
At 3.40, the hour hand and the minute hand of a clock form an angle of :
- $110 ^{\circ}$
- $115 ^{\circ}$
- $130 ^{\circ}$
- $155$
Correct

Angle traced by hour hand in 6 hours = 360 $^{\circ}$

Angle traced by hour hand in 12 hours = $(\frac{360}{12}\times\frac{11}{3})^{\circ} = 110^{\circ}$

Angle traced by minute hand in 60 min.=360 ${\circ}$

Angle traced by it in 40 min. = $(\frac{360}{60}\times 40)^{\circ} = 240^{\circ}$

$\therefore$ Required angle (240-110) $^{\circ}$ = 130 $^{\circ}$

Incorrect

Angle traced by hour hand in 6 hours = 360 $^{\circ}$

Angle traced by hour hand in 12 hours = $(\frac{360}{12}\times\frac{11}{3})^{\circ} = 110^{\circ}$

Angle traced by minute hand in 60 min.=360 ${\circ}$

Angle traced by it in 40 min. = $(\frac{360}{60}\times 40)^{\circ} = 240^{\circ}$

$\therefore$ Required angle (240-110) $^{\circ}$ = 130 $^{\circ}$
Question 19 of 20

19. Question
1 points
How many times do the hands of a clock coincide in a day ?
- 10
- 23
- 22
- 44
Correct

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1,they coincide only one,i.e. at 12 o'clock).
$\therefore$ The hands coincide 22 times in a day.

Incorrect

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1,they coincide only one,i.e. at 12 o'clock).
$\therefore$ The hands coincide 22 times in a day.
Question 20 of 20

20. Question
1 points
How many times in a day, the hands of a clock are straight ?
- 21
- 14
- 44
- 84
Correct

In 12 hours, the hand coincide or are in opposite direction 22 times.

$\therefore$ In 24 hours, the hands coincide or are in opposite direction 44 times a day.

Incorrect

In 12 hours, the hand coincide or are in opposite direction 22 times.

$\therefore$ In 24 hours, the hands coincide or are in opposite direction 44 times a day.