** Key facts: Generally there are four components in a clock (i) Dial** is a circular or square shape plaque that has digits or points from 1 to 12.

**(ii) Hour Needle**, the Hour needle is slightly shorter than the minute Needle and it expresses the time in Hours as if the needle of hour is at 4’and the needle of minute is at ’12 ‘, Then it will indicate the time as 4 O,clock.

** (iii) Minute Needle **minute Needle is slightly larger than the hour needle and plays a supporting role in conveying the certainty of time together with the hourly needle, such as if the hours needle is on ‘6’ and the needle of minute is at ’12 “, then it will be indicative that the time is ‘6’ o.clock. But if the hourly needle is slightly ahead of ‘6’ and the minute needle is on ‘3’, then it will be indicate that the time in clock is 6:15 .

**(iv) Second dipping ** Usually the needle of the second is slightly larger and thin than the minute dipping. It plays the role of assistants in the deviation of both the hours and minutes. The measurement of the entire circumference of the clock dial is 360 °, that is, we can say that if a needle moves clockwise from ’12’ to ’12 ‘then it is indicative that the needle has traveled the path of 360° .

The measurement of the angle between any two adjacent digits of the clock is ’30°’, for example, the angle between ‘2’ and ‘3’ is ’30°’.

Deviation of degrees (in degrees) per minute is as follows

Second dipping ⇒ 360° per minute

Minute dipping ⇒ 6° per minute

Hour dipping ⇒ 1/2° per minute

Generally three types of questions are asked from this chapter

**Type 1 **

Normally, the letters of the English alphabet, or the opposite alphabet, in the corresponding direction of the letters of the alphabet are placed in clockwise or anti clockwise direction, instead of a fixed number of letters. The questions related to this matter will be asked in this chapter.

Now, let’s take a closer look at the format of the questions and its interpretive solution under the arrangement of the letters.

** Example 1. **If the letters on the clock dial are replaced by English alphabet in such a way that the letter “G” comes in place of the number “2” “H” instead of the letter ‘3’, and the sequence of change continues in the same way, what will become at the place of the number 12?

(a) S (b) Q (c) M (d) N

** Solution: **(b) According to the question we see that the letter ‘G’ is used for the Number “2”, then the letter ‘H’ is used for the Number 3, similarly, for the number ‘4’, the letters of the English alphabet ‘I’ Will be used.Therefore

2 ⇒ + 5 ⇒ 7

3 ⇒ + 5 ⇒ 8

Similarly, 12 ⇒ + 5 ⇒ 17

Here we see that the numeric value is replaced with English alphabet with a certain difference at its position. So the numeric value of the letters used in the English alphabet for ’12’ will be (12 + 5) = 17 and we know that in the English alphabet ‘Q’ is at the numeric value 17.

Hence the desired letter ‘Q’ will be. .

** Example 2.** If the letters of the English alphabet are arranged in place of the digits located on the clock dial, Like letter ‘U’ came in place of the number ‘6’, letter ‘R’ came in place of the number ‘5’ , similarly the letter ‘O’ comes in place of number ‘4’ and if the sequence of changes continues in the same way, then what will be at the place of the letter ‘1’?

(a) G (b) F (c) I (d) K

**Solution:** (b)

6 ⇒ × 3 + 3 ⇒ 21

5 ⇒ × 3 + 3 ⇒ 18

4 ⇒ × 3 + 3 ⇒ 15

Similarly, 1 ⇒ × 3 + 3 ⇒ 6 = F

Here we are seeing that the number obtained by adding 3 in its three times to each digit, the alphabet used for the same number in alphabetical order has come for that number. Similarly, on adding 3 to three times of the number ‘1’, the number is 6 and the letter ‘F’ is in the sixth place in alphabetical order. So the desired letter will be ‘F’.

**Type 2 **

The degree related questions are given at a specific time and on the basis of that exact time, the candidate has to decide how many degree of angle between the hour and minute needle is formed during the given time.

To easily solve such questions, please take a closer look at the key sources below. The minute here implies the number used in the place of minute needles, such as – 20 minutes, 4.30 minutes, 6.35 minutes, 7 etc.

If the minute needle is behind the hourly needle

Desired degree = difference in number between minutes and hour × 30 ± min/2

Minutes given in question – If minute needle is ahead of the hour needle.

⇒ Now, Lets see the questions asked in this chapter for clarification of the above facts. Carefully observe the questions and their interpretive solution.

**Example 1.** If the time is 7:30 in a clock, then determine the angle formed between the hour and minute needles?

(a) 120° (b) 95° (c) 45° (d) 75°

** Solution: **(c) Time = 7:30

In this situation the position of hour and minute needles will be on 6 and the hourly needle will be in between 7 and 8.

Hour dipping distracts ½° in one minute

Deviation of hourly dipping in 30 minutes = 1/2 × 30 = 15°

I.e. hour dipping will be 7 to 15°.

The difference in points from the position of the needles = 7 – 6 + 15° = 1 + 15°

The difference of 1 = 30°

1 + 15° = 30° + 15° = 45°

Therefore the desired angle = 45° formula as intended = (7 – 6) × 30° + 30°/2

= 1 × 30° + 15° = 30 + 15° = 45°

** Example 2. **If the time is 5:45 in a clock, Then what is the angle formed between minute and hour needle at that time?

(a) 97½° (b) 120° (c) 105° (d) 142½°

** Solution: **(a) Time = 5:45 In this situation the position of hour and minute needles will be as: minute needle is at 9 and the hourly needle will be above 5. Also the minute needle is ahead of the hour dipping.

So now with the formula,

Expected angle = (9-5) × 30° – 45/2

= 120° – 22½° = 97½°

** Example 3. **If The time is 12:20 in a clock, Then what is the angle formed between minute and hour needle at that time?

(a) 110° (b) 127° (c) 97½° (d) 84°

** Solution: **(a) Time = 12:20

The hour needle will be on 12 and at 20 minutes the needle of minute will be 4. Also the minute needle will be ahead of the hourly dipping.

By formula, intended angle = (4 – 0) × 30 – 20/2

120 – 10 = 110 °

** ⇒ Note – **When the hourly needle is at 12, then counting it as ‘0’, we find the difference in the number between the minutes and the hours.

** Example 4.**If The time is 4:47 in a clock, Then what is the angle formed between minute and hour needle at that time?

(a) 97½° (b) 83½° (c) 110° (d) None of these

** Solution: **(d) According to the formula, angle

** Example 5.**If The time is 9:22 in a clock, Then what is the angle formed between minute and hour needle at that time?

(a) 119° (b) 145° (c) 149° (d) 161°

Solution: (C) Expected angle

**Type 3 **

The plane mirror is divided into two sections based on its position.

** (i) vertical mirror – **A position of plane mirror placed in a vertical position at an angle of 90 ° relative to any horizontal plane, such a mirror Is called a vertical mirror. The reflection of the thing placed in front of such a mirror appears to be overturned, that is, the part of the object in the original pattern is on the left, in the image it is on the right side and the portion on the right is transferred to the left in the image. Carefully observe the diagrams below to understand it well.

In the diagram given here, we see that the hourly needle in the original pattern is located at ‘8’ on the left side of the clock but in the mirror ‘AB’, it seems to be on the right side of the clock as a fictitious model, while the minute the needle seems to be stable in its own place even if it is reversed. because it is perpendicular.

Actually, this certainly affirms that in the perpendicular mirror the left part of the object appears to be the right and right part of the object appears to be the left.

**(ii) Horizontal Mirror –** A horizontal mirror that is positioned in a parallel position of plane mirror such as a horizontal plane is called a horizontal mirror. The image of the object placed in front of such a mirror appears to be inverted, i.e. the shape of the top will appear as bottom and bottom appears on the top, but the left part will remain left and the right part will remain right. Observe the diagram below to understand it well.

Here we are seeing that in the original pattern of the above diagram, the hourly needle is slightly lower than 9 on the left side of the clock and the minute needle is located on the right side of the clock from 3 to one place above 2, but in the form of this hypothetical model in the mirror AB, The hourly needle is as above the number ‘9’ as it was lower in the original and the needle of minute appeared as below below 3 as it was appeared below in the original. Thus, there is definitely a confirmation that in the horizontal mirror, the left part of the object appears to be left and right appears to be right but it flips the image sides relative to 9 and 3.

**Major rules for resolving vertical mirror questions **To solve the questions related to the mirror vertically, a specific time base 12:00 should be used as the following form.

If the time given is real time

Mirrored (hypothetical) time = 12:00 – real time

Like – if the real time = 5:30 then the hypothetical time = 12:00 – the actual time = 12:00 – 5:30 = 6:30

If the time given is a hypothetical time, then the real time = 12: 00 – the hypothetical time

As if hypothetical time = 4: 15

Real time = 12:00 – 4: 15 = 7:45

Now, let us carefully review some of the key examples related to this.

** Example 1. **In the triloki’s clock, Dots have been marked in place of the digits. If reflected image of a mirror shows the time as 12:35, then was the actually time at that time in his watch?

(a) 1: 35 (b) 11:25 (c) 0: 35 (d) 12 : 30

** Solution: **(b) Real-time = 24: 00 – 12: 35 = 11: 25

**⇒ Note** – It is necessary to note that it is taken from hour if it is necessary to borrow the time of the minute in relation to time. The time taken is always taken as 60 minutes i.e. one hour. In this situation Hours are less than 1 hour after its original condition. In addition to this, if the time limit is reduced from 12:00 pm to 00:00, or if you get a negative hour, then the time base will not be kept at 12: 00 p.m., but time base for this is 24:00 Assuming the time will be reduced by giving reasonable time. Like – 24:00 – 12: 35 = 11: 25

** Example 2. **Dots are marked in place of numbers on a clock. If this clock is showing 6:20 minutes, then when it will be placed in front of a mirror,what time it will show in the image of the mirror?

(a) 5:40 (b) 4:55 (c) 5:45 (d) 5:20

** Solution: **(a) Reflected time = 12:00 – 6:20 = 5:40

** Major rules for solving horizontal mirrors / water-related reflections **

** I. **Usually the minute needles becomes 60° and hour needles becomes distracted from its place ½° per minute. Like, if you are getting 7:30 minutes in a clock,

In this situation, the Hours needles points 15 ° above to 7 (i.e. between 7 and 8) and the minute needle’s position will be at ‘6’. But in the related questions of the horizontal mirror, the diversion of hourly Needles should not be consider. Because in such a situation, real time can not be accurately determined by the reflected time or reflected time from the real time. Carefully study the frequency of the clock given below for clarification of the above facts.

Here we are seeing that in the actual or fictitious situation, the hourly needle is 15 ° above to ‘7’ to i.e. in between 7 and ‘8’. and the minute’s needle is indicated at place of ‘6’, however, the Hourly needle in reflected time is reversed on the basis of the physical condition of real time, i.e. between 10 and 11, and the minute needle is described in place of 12. If considered, the horizontal mirror shape in the case of 7:30 it should definitely be in accordance with the reflected time pattern above, but it is against the principle of time. That is because the minute needle is on ’12’ and the Hourly needle is between ’10’ and ’11’ exactly the opposite of the principle of deviation of hour and minute needles which is not possible in any situation. Therefore, on the basis of the above facts we arrive at the conclusion that in the questions related to the horizontal mirror = 8:20, the need for hourly Needle should never be considered while distracting with the principle of time.

**II. **The image of the object in the horizontal mirror is always made upside down, that is, the upper part of the object appears as ‘lower part’ in the mirror and ‘lower part’ appeared in the form of ‘upper part’.

Under the horizontal mirror, the original shape is reversed in the image, but its left and right parts do not change with each other, which confirms that the image in the horizontal mirror only appears inverted.To solve the horizontal issues, firstly consider ‘9’ and ‘3’ as the time base, on which we can easily change the reflected time or any reflection time in to ‘real time’. In this way You can easily determine the intended time.

In the above figure, we are seeing that the clock is at 8:20 minutes and in this situation, the Hourly needle is one place below 9 i.e. 8 and the minute needle is placed one place below 3 i.e. 4 . But in the mirror The Hour Needle appears one place above 9 i.e. at 10 and the minute needle appears one place above 3 i.e. at 2.

Therefore, on the basis of these facts, it is confirmed that time is as below the real time from the base 9, as higher in the mirror from the base ‘9’. It appears to be down converted and precisely this factor also applies in the perspective of time base ‘3’ i.e. the same time needle appears above / below the mirror relative to the real time.

Now let us carefully review the format of these related questions.

**Example 1. **If you look at Ghauri in a horizontal mirror, the reflected time appears to be 10:20 in its clock, then find out that what is the real time in its clock ?

(a) 10:20 (b) 8:10 (c) 5:40 (d) 1 : 10

** Solution:** (b) Reflect time = 10:20

In the horizontal mirror, the position of the hour of Needle is at 10, one place above the time-base = ‘9’ and the position of minute Needle is one place down = “3 ” i.e 4.

Therefore, in the real-time, the location of the hour needle = ‘8″ below the position of ‘9’ and the minute needle’s position =”2″at one place above ‘3’

Thus, real time = 8:10

** Example 2. **In a clock, Dots are marked in place of Numbers. If the clock is just at 12 o’clock, then after seeing in a horizontal mirror, What is the time appeared in that clock?

(a) 6:30 (b) 12:00 (c) 12:30 (d) 11 : 45

** Solution: **(a) 12 o’clock in the actual clock means hours Needle and minute Needles will both be present on ’12 ‘.

So when it is seen in a horizontal mirror, the Hour and minute needle will be present on ‘6’.

Hence the intended time in the horizontal mirror = 6:30

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