**Clock Reasoning**

A clock is an instrument used for indicating and maintaining the time. It is an electronic device that presents the duration of an hour, minute and second.

*Different types of question covered in this chapter are as follows.*

**Angle Between the Hands of the clock****Position of Hands of the clock****Faulty clocks****Time Gained or lost by the clock**

**Clock Reasoning Tricks**

1) To solve questions related to the angle between the hands of clock the formula for the same will be 160H - (11M/2) = ΘI. Where H = Hour, M= Minutes, and Θ is the angle between the hands of the clock.

2) Coincide means 0 angle between two hands or when the hands are together. There is 1 coincide per hour except 11 to 1 AM/PM. Therefore there are 11 coincide in 12 hours and 22 coincides in 24 hours. The first coincide is at 12 AM and the next happens at 1:05 AM.

3) For ques related to mirror images of clock, if the clock is at 12 hours then candidates must subtract the given time from 11:60 hours where if it is 24-hour clock then candidate must subtract time from the 23:60 hours.

4) For the ques related to water images, if the minute is less than 30 then candidate subtract given time from 18:30 hours whereas if it is more than 30 than candidates must subtract given time from 18:90 hours.

**Clock Reasoning Formulas**

The clock represents two things. i.e., minutes an hour. A minute is a unit of time equal to 1/60^{th} of an hour or 60 s i.e, **1 min = 60 s.**

**Clocks Concepts :**

- The dial of the clock is circular in shape and was divided into 60 equal-minute spaces
- 60-minute spaces trace an angle of
**360**^{0}. Therefore, 1minute space traverses an angle of 6^{0} - In 1 hour, the Minute hand traverses
**60-minute space or 360**, hour hand traverses 5-minute space or 30^{0}^{0} - The hands of the clock are
**perpendicular**in 15-minute spaces apart - The hands of the clock are in a straight line and
**opposite**to each other in**30-minute**spaces apart. - The hands of the clock are in a straight line when they coincide or opposite to each other.
- The hands of the clock are perpendicular to
**each other for 22 times in 12 hours**and for**44 times**in a day. - The hands of the clock are
**opposite**to each other for**11 times in 12 hours**and 22 times in a day. - The minute hand gain
**55 minutes**over hour hand per hour.

Hence x minute space to be gained by minute hand over hour hand can be calculated as x.(60/55) or x.(12/11)

**Ex: **At what time between 2'O clock and 3'O clock the hands of the clock Ware opposite to each other.

1. 34( 6/11 ) past 2'Oclock

2. 43( 7/11 ) past 2'Oclock

3. 56( 8/11 ) past 2'Oclock

4. 64(9/11past 2'Oclock**Solution:**

At 2'O clock, the minute hand will be at 12 as shown below

The minute's hand to coincide with the hour hand it should trace at first 10 minute spaces and then the hands of the clocks to be opposite to each other minute hand should trace 30-minute spaces i.e. totally it should gain 10+30=40 minute spaces to be opposite to that of the hour hand

We know that,

Minute hand gains 55-minute spaces over hour hand in 1 hour

Therefore, Minute hand gain 40-minute spaces over hour hand in 40 × (60/55) = 43(7/11)

Hence the hand of the clock & minute will be opposite to each other at 43( 7/11 ) past 2'Oclock

Therefore, **the Correct option is 2'**

**When the clock is too fast, too slow**

- If a clock or watch indicates 6 hr 10 min when the correct time is 6, it is said that the clock is 10 min too fast. If it indicates 6. 40 when the correct time is 7, it is said to be 20 min too slow.

Now let us have an example based on this concept

**Ex: **My watch, which gains uniformly, is 2 min, & show at noon on Sunday, and is 4 min 48 seconds fast at 2 p.m on the following Sunday when was it correct?

**Solution:** From Sunday noon to the following Sunday at 2 p.m there are 7 days 2 hours or 170 hours.

The watch gains 2+4^{4}/_{5}min in 170 hrs.

Therefore, the watch gains 2 min in (2 *170 * 5/34) hrs i.e., 50 hours

Now 50 hours = 2 days 2 hrs.

Therefore, 2 days 2 hours from Sunday noon = 2 p.m on Tuesday.

**Problems On angles**

Before we actually start solving problems on angles, we need to know a couple of basic facts clear:

**Speed of the hour hand**= 0.5 degrees per minute (dpm)**Speed of the minute hand**= 6 dpm- At ‘n’ o'clock, the angle of the hour hand from the vertical is 30n

Example: 1 *What is the angle between the hands of the clock at 7:20*

**Solution:**

At 7 o'clock, the hour hand is at 210 degrees from the vertical.

In 20 minutes,

Hour hand = 210 + 20*(0.5) = 210 + 10 = 220 {The hour hand moves at 0.5 dpm}

Minute hand = 20*(6) = 120 {The minute hand moves at 6 dpm}

Difference or angle between the hands = 220 – 120 = 100 degrees

**Example:2 ***Find the reflex angle between the hands of a clock at 05.30?*

**Solution:**

*Angle between X and Y =|(X*30)-((Y*11)/2)|*

Angle between hands at 5:30

**Step 1**: X=5 , Y=30

**Step 2**: 5*30=150

**Step 3:** (30*11)/2 = 165

**Step 4:** 165-150=15

Thus, the angle between hands at 5:30 is 15 degrees.

**Example : 3 ***At what time 3&4’o clock in the hands of the clock together.*

**Solution:**

Approximately we know at 03:15 hands of the clock together

So 15*60/55=16.36 min

**Problems on incorrect clocks**

Such sort of problem arises when a clock runs faster or slower than expected pace. When solving these problems it is best to keep track of the correct clock.

**Example: ***A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day?*

**Solution:**

The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour.

From 8 AM to 10 PM on the same day, time passed is 14 hours.

In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.

So, when the correct time is 10 PM, the watch would show 10: 23: 20 PM

**Important Points to remember: **

- Two right angles per hour (Right angle = 90, Straight angle=180)
- Forty-four right angles per day
- Between every two hours, the hands of the clock coincide with each other for one time except between 11, 12 and 12, 1. In a day they coincide for 22 times.
- Between every two hours, they are perpendicular to each other two times except between 2, 3 and 3, 4 and 8, 9 and 9, 10. In a day they will be perpendicular for 44 times.
- Between every two hours they will be opposite to each other one time except between 5, 6 and 6, 7. In a day they will be opposite for 22 times.

**Clock Questions for SSC**

1. How many times are the hands of a clock at right angle in three days?

A. 48B. 72

C. 44

D. 132

Answer ||| D

2. At what time between 11 and 12 o’clock will the hands of a clock be at the right angle?

A. 11: 43B. 11: 47

C. 11: 45

D. 11: 47

Answer ||| A

3. What will be the angle between minute hand and hour hand at 7:39?

A. 6B. 4

C. 4

D. 6

Answer ||| C

4. How many times are the hands of a clock at right angle in the March month of a year?

A. 1348B. 1364

C. 1244

D. 1472

Answer ||| B

5. In 45 minutes, the minute hand gains over the hour hand by ___________?

A. 217 degreeB. 237 degree

C. 257 degree

D. 247 degree

Answer ||| D

6. At what time between 8 and 9, are the hands of a clock coincide?

A. past 8B. past 8

C. past 8

D. past 8

Answer ||| D

7. At what time between 1 and 2 will the hands of a clock coincide?

A. past 1B. past 1

C. past 1

D. past 1

Answer ||| D

8. A clock is started at noon. By 40 minutes past 4, the hour hand has turned through _______?

A. 180°B. 130°

C. 140°

D. 120°

Answer ||| C

9. Find the angle between the minute hand and the hour hand of a clock when the time is 8 .35?

A. 47(1/2) degreeB. 57(1/2) degree

C. 67(1/2) degree

D. 37(1/2) degree

Answer ||| A

10. Calculate the angle between the two hands of the clock when the clock shows 5:25 PM?

A. 12.5 degreeB. 11.5 degree

C. 13 degree

D. 15 degree

Answer ||| A

**Clock Reasoning Questions for SSC CGL**

11. Find the angle between the minute hand and the hour hand of a clock when the time is 6.50?

A. 95 degreeB. 70 degree

C. 80 degree

D. 85 degree

Answer ||| A

12.In 55 minutes, the minute hand gains over the hour hand by ___________?

A. 302 degreeB. 302 degree

C. 346 degree

D. 252 degree

Answer ||| B

13. If the minute hand of a clock points towards the east at 12:00 a.m., then in which direction will the minute hand point at 7:30 a.m. in the same clock?

A. South-EastB. South-west

C. North-West

D. North-East

Answer ||| C

14. At what angle the hands of a clock are inclined at 40 minutes past 9?

A. 30°B. 65°

C. 58°

D. 50°

Answer ||| D

15. What could be the water image of 12:30?

A. 06:00B. 05:30

C. 06:30

D. 05:00

Answer ||| D

16. Two clocks are set at 12 AM. The first clock gains 5 minutes every hour. Second slows down by 1minute every hour. After how many days will both the clocks show the same time again?

A. 11 daysB. 10 days

C. 9 days

D. 8 days

Answer ||| B

17. At what time between 9:30 and 10:05 will the hands of a clock be at right angles?

A. 9: 40minB. 9: 49min

C. 9: 40min

D. min

**Clock Questions PDF**

We have compiled the **“Clock Questions for SSC and Railway Exams”**. These questions have been asked in previous years' papers too. Candidates who are willing to appear in any of the SSC and Railway exams can download Clock Questions PDF so that they get all the important questions in one place. And it will become very easy for aspirants to practice and revise before the exam.

**> Clock Questions PDF (To be activated)**

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