- In the given table, we have discusses some examples on the basis of different relationships established among them.
Country & Currency
Quantity & Unit
Instrument & Measurement
Unit & Group
Animal & Baby
Male & Female
Animal & Movement
Animal/thing & Sound
Unit & Class
Unit & Home
Game & Venue
Profession and Tool
Product & Raw Material
Unit & Part
Study & Topic
Types of Analogy
- Analogous pair: Such questions give the relationship between a pair; the first element of the second pair is given and we have to find the second element of the second pair based on similar relationship given by first pair.
1) Oasis: Sand ∷ Island:?
Explanation: Here, first pair is ⇒ “Oasis: Sand” and second pair is “Island:?”. And, “∷” sign means first pair and second pair share similar relationship. ‘Oasis’ is a mass of water amidst ‘Sand’ similarly ‘Island’ is a mass of land amidst ‘water’. Note: It’d be Island: Sea had the first pair been Oasis: Desert. We’re given the name of thing desert is made of i.e. Sand. So, we’ll use the name of thing Sea is made of i.e. Water.
2) Annihilation: Fire ∷ Cataclysm
Explanation: Here, ‘Annihilation’ i.e. total destruction is the result of ‘Fire’. So, ‘Cataclysm’ i.e. the rising of a body of water and its overflowing onto normally dry land is the result of ‘flood’.
- Simple Analogy: In such questions a simple statement is given where a relationship is given and we’re asked the second element for the term given in question, like the example below:
1) Sweet is to Chocolate as Book is to….?
Here, Chocolate can be sweet or bitter but ‘Sweet’ is the enlarged form of chocolate. Similarly, ‘Encyclopedia’ is an enlarged form of a ‘book’.
- Choosing the analogous pair: In such questions, a pair is given in the question and we’ve to find a suitable pair from the options given that resembles the similar relationship as in the question like the examples below:
1) Borrow: Steal
a) Enter: Trespass
b) Tell: Speak
c) Ask: Beg
d) Hit: Kill
Here, for both ‘borrowing’ and ‘stealing’ we take someone else’s thing. The only difference being that the first thing we take is with the permission of another while second thing is taken without the permission of another. Similarly, among all the options, we see this option is seen in ‘Enter: Trespass’ where we ‘enter’ after taking permit while ‘trespassing’ is done without any permit whatsoever.
2) Cool: Frigid
a) Livid: Lurid
b) Pool: Placid
c) Tepid: Torrid
d) Lack: Abundant
Here, ‘Frigid’ means extremely cold. So, in Cool: Frigid, second is the extreme version of another. Let’s check the meaning of all options given:
a) Livid ⇒ Discolored beneath the skin: Lurid⇒ Ghastly pale ⇒ This doesn’t give extreme version of paleness.
b) Pool⇒ A small lake : Placid⇒ a body of water free from disturbance by heavy waves ⇒ This doesn’t give extreme version of pool.
c) Tepid⇒ Moderately warm: Torrid⇒ Extremely hot ⇒ Torrid is the extreme version of Tepid.
d) Lack: Abundant⇒ Present in great quantity ⇒ These two are opposite not extreme version.
We can see that only option c) fulfills the criteria.
- Multiple word analogy: These are the type of questions discussed above with the only difference being that here three elements are given in a pair instead of two and we have to select the suitable option. Like the example below:
1) Music: Guitar: Performer
a) Dance: Tune: Instrument
b) Food: Recipe: Cook
c) Patient: Medicine: Doctor
d) Trick: Rope: Acrobat.
In, Music: Guitar: Performer, ‘Performer’ plays ‘Music’ on ‘Guitar’. So, III element is playing/doing I element on II element.
From options, we can clearly see that this pattern is followed only in option d) i.e. Acrobat (An athlete who performs acts requiring skill) performs ‘Tricks’ on a ‘Rope’.
- Number-based analogy: Till now, we saw the analogy based on words now we’ve questions based on numbers too like shown below:
1) Completing analogous pair.
25: 37 ∷ 49:?
Here, in 25: 37 the pattern can be explained as where is the first element as 25 = 5^2 and is the second element as 36 = (5+1)2 + 1.
For 49, we know that 49 = 72 so second element = = 65 which is option d).
2) Choosing the analogous pair.
a) 30: 100
b) 23: 72
c) 19: 58
d) 11: 43
In 7: 24, 24 = 7×3 + 3 i.e. the relationship can be shown as
Similar relationship can only be seen in option b) 23: 72 where 23×3 + 3 = 69 + 3 = 72.
- Multiple number analogy: It’s just like multiple-word analogy:
1. (9, 15, 21)
a) (10, 14, 21)
b) (7, 21, 28)
d) (4, 8, 12)
In (9, 15, 21) the pattern given is as 15 = = 15 where 9 and 21 are 1st and 3rd numbers respectively.
Similar relationship can only be seen in so option d) where 8 (second no.) = = 8
- Alphabet based analogy. In these types of questions, two words that are group of random letters are related to each other in some way. We’re supposed to complete the analogous pair based on that relationship:
1. FJUL: BOQQ∷ LHRX: ?
The relationship between FJUL: BOQQ can be illustrated as:
If we do a similar operation on LHRX we can see the following:
Hence, option d) is the answer.
- Mixed analogy: These types of questions mixed alphabet and number like shown below:
Here, in , T is 20th element in the alphabet series while J is 10th so Similarly, X is 24thelement in alphabetical series while H is 8th so So,
Word formation by unscrambling letters
- In such questions, usually jumbled letters are given various types of questions are asked on the unscrambled word thus formed. For example:
a) VARSTE ⇒ Choose the correct order of letters which are required to form the correct word.
i) 2, 3, 1, 6, 4, 5
ii) 3, 2, 4, 5, 6, 1
iii) 4, 5, 2, 3, 1, 6
iv) 6, 3, 4, 5, 2, 1
Here, we’ve to create the correct word and ‘V’ has been labeled as 1, ‘A’ as 2, ‘R’ as 3, ‘S’ as 4, ‘T’ as 5 and ‘E’ as 6.
On observing we can see the correct word is STARVE. Hence, the correct order is 4(for S) 5(for T) 2316 ⇒ 452316 ⇒e. option iii) is correct.
b) Unscramble the words in options and find the odd-one out:
Let’s unscramble the options:
i) UPJM⇒ JUMP
ii) WKLA ⇒ WALK
iii) PEELS⇒ SLEEP
iv) UNR⇒ RUN.
We can see that all options except PEELS or SLEEP are active actions while sleep is a passive activity. So, option iii) is odd-one out.
c) Unscrambled the word in question and find the option most similar in meaning to rearranged word:
I T G N D L E I
On unscrambling the word we can see that the given word is DILIGENT. And, synonym for diligent is Laborious so option iii) is the answer. Similar question on antonym can also be asked.
2. Word formation using letters of a given word:
a) Using certain letters of a word:
If it’s possible to make a meaningful word from 2nd,5th, 6th and 7th letters of the word GENEROSITY, then which will be the first letter of that word? Mark X if no such word can be formed, M if more than 1 such word can be formed.
Here, the word = GENEROSITY
2nd,5th, 6th and 7th letters = E, R, O and S
Words starting with E = none, with R = ROSE, with O = ORES, with S = SORE
Clearly, we can see that more than 1 i.e. 3 words can be formed so we’ll mark ‘M” i.e. option iv) as the answer.
Note: Had the ROSE been the only word getting formed then we’d have marked option i) i.e. R as answer because R is first letter of only word ROSE.
b) Using certain letters of a series:
U H O L Y F G W Z B A S R
Above a series is given, how many meaningful word can be formed from 3rd letter from left, 4th letter from right, 6th letter from left and 9th letter from right?
Here the series: (left) U H O L Y F G W Z B A S R (right)
3rd letter from left = O, , 6th letter from left = F,
4th letter from right = B, 9th letter from right = Y
Given letters = O, F, B, Y
We can see no such meaningful word can be formed using the aforementioned alphabets. Hence, we’ll mark ‘none’ i.e. option iv) as the correct answer.
Statement and Conclusions
- The Reasoning section of every competitive exam includes questions from the topic “Statement & Conclusion”. This topic is considered to be quiet important and every year a good number of questions are asked from this topic. It is considered to be a very scoring topic. We are providing you with all the important tools to solve Statement & Conclusion questions easily and accurately.
- A statement is a group of words arranged to form a meaningful sentence. A conclusion is a judgment or decision reached after consideration about the given statement.
Different types of questions covered in this chapter are as follows.
- One statement with Two Conclusion Based
- More than Two Statements and Conclusion Based
A conclusion is an opinion or decision that is formed after a period of thought or research on some facts or sentence stated by someone. A consequent effect has always to be analysed before reaching to the final result or conclusion of a given premise. This requires a very systematic and logical approach.
- Statement: Some people say that good thought come in their mind in the morning.
- Conclusion: Thoughts come in mind, in the morning only.
Now, consider the statement, the word ‘some’ used in the statement does not mean ‘all’. It means some people say not all. Hence, according to some people, good thoughts come in their mind in the morning but thought can come any time in the mind of other people, so, the conclusion that ‘thoughts’ come in mind, in the morning only is not valid. Also, the word used ‘only’ makes the conclusion totally invalid because its restricts that the thought can come only in the morning.
To reach to a conclusion think only about the information given in the statement. There is no need to use, assume anything else or add any further or extra information from outside but the established facts cannot be denied like the Sun always rises in the East, a day consists of 24 h etc.
- If statement is formed with two or more sentences, then there should be no mutual contradiction in sentence.
- Statements and conclusion should not go against established facts and prevailing notious of truth.
- If definitive words like all, always, atleast, only, exactly and so on are used, then such words make the conclusion invalid or ambiguous.
- Always read very carefully and try to find key words as key words play an important role in analysing valid and invalid conclusions.
- If the conclusion is provided with a stated example, then the conclusion is invalid.
Type 1: One Statement with two Conclusions Based.
- In this types of questions, a statement is given followed by two conclusion . the candidate is required to find out which of conclusion follows the given statement and select the correct option accordingly. Following examples will give a better understanding about the type of questions asked.
Directions ( 1 – 2): In each of the following questions, a statement is followed by two Conclusions I and II.
(a) if only Conclusion I follows
(b) if only Conclusion II follows
(c) if either I or II follows
(d) if neither I nor II follows
Ex 1: Statement: Parents are prepared to pay any price for an elite education to their children.
I. All parents these days are very well off.
II. Parents have an obsessive passion for perfect development of their children through good schooling.
It may be conclusion from the statement that since parents want a perfect development of their children through good schooling therefore they are prepared to pay any price for a good education but the statement does not give sense of the parents being very well off. Hence, only Conclusion II follows.
Ex 2 : Statement: Interview panel may select a student who is neither possessing the abilities of desired level nor any value and assumption.
I. Inclusion of experts in interview panel does not ensure that the selection will be made properly.
II. Interview procedure of admission has some limitations.
The statement clearly means that inclusion of experts does not ensure proper selection. It also indicates limitation of interview procedure for admission. Here, both the conclusions follow.
Type 2: More Than Two Statements and Conclusion Based
In this type of questions, a statement / statements I / are given followed by some conclusion. Choose the conclusion which follows the given statement.
Directions (1 - 2): Which of the conclusion can be drawn from the statement?
Ex 1: Statement: Many business offices located in buildings having two to eight floors. If a building has more than three floors, it has a lift.
(a) All floors may be reached by lifts
(b) Only floors above the third floor have lifts
(c) Fifth floor has lifts
(d) Second floors do not have lifts
It is clear from the given statement.
Ex 2: Statements
Karan Johar is a good director.
Directors are intelligent.
(a) All intelligent are directors
(b) Karan Johar is intelligent
(c) Both (a) and (b)
(d) None of these
As directions are intelligent and karan Johar is good director, so Karan Johar is intelligent.
- Family or Blood Relationship means persons connected by relations like – father-mother, son daughter, brother-sister, grandfather-grandmother, uncle-aunty, nephew-niece, brother-in-law sister-in-law etc.
- The list can go on and on adding members from father’s side and mother’s side etc.
- Questions in Test of Reasoning on Family /Blood Relationship are about the relationship of a particular person with another person of the family, based on the chain of relationships between other members of that family
- Family/Blood Relation Tests are an exercise to test the candidate’s ability to comprehend and come to the crux of an issue from complex, lengthy and unclear data.
- ‘Ram’ is the father of ‘Kusha’ but ‘Kusha’ is not his son. ‘Mala’ is the daughter of ‘Kusha’. ’Shalaka’ is the spouse of ‘Ram’. ‘Gopal’ is the brother of ‘Kusha’. ‘Hari’ is the son of ‘Gopal’. ‘Meena’ is the spouse of ‘Gopal’. ‘Ganpat’ is the father of ‘Meena’. Who is the granddaughter of ‘Ram’?
(1) Hari (2) Mala (3) Meena (4) Shalaka
‘Mala’ is the daughter of ‘Kusha’ and ‘Ram’ is the father of ‘Kusha’. So, ‘Mala’ is the granddaughter of ‘Ram’. Hence, answer is (2) Mala.
Some Common Terms
- Meaning of some terms often used in questions on family relationship are given below:
a) Parent – Mother or father
b) Child – Son or daughter (even if an adult)
c) Sibling – Brother or sister (Including half brother and half sister – one parent in common)
d) Spouse – Husband or wife
Aunt, Uncle, Niece and Nephew
- Most English speakers use “uncle” for any of four relationships: father’s brother, mother’s brother, father’s sister’s husband, or mother’s sister’s husband.
- Again, “aunt” in English could mean father’s sister, mother’s sister, father’s brother’s wife, or mother’s brother’s wife.
- Brother’s or sister’s son is called nephew. Brother’s or sister’s daughter is called niece.
- Children of aunt or uncle are called cousins.
Relationships Involving the Term ‘-in-law’
- Any relationship term ending with -in-law indicates that the relationship is by marriage and not by blood. In other words, -in-law will be a blood relative of the spouse.
- In-law relationship terms are always written with hyphens. And the plural is formed on the part before the “-in-law”;
For example, “brothers-in-law” and not “brother-in-laws”. The only exception is the general term “in-laws”, which is always plural.
Father-in-law, Mother-in-law, Son-in-law and Daughter-in-law
- Father-in-law is the father of spouse; mother-in-law is the mother of spouse. If parents get divorced and remarry, their new spouses are called stepparents, not mother-in-law and father-in-law.
- The husband of daughter is son-in-law; the wife of son is daughter-in-law. If spouse has children from a previous marriage, those are called stepchildren, not sons-in-law or daughters-in-law. The person is their stepfather or stepmother, not their father-in-law or mother-in-law.
Brother-in-law and Sister-in-law
- Brother-in-law” and “Sister-in-law” each have two or three meanings as follows:
a) Sister-in-law could be
i) The sister of spouse, or
ii) The wife of brother, or
iii) The wife of spouse’s brother.
b) Similarly, Brother-in-law could be
i) The brother of spouse, or
ii) The husband of sister, or
iii) The husband of spouse’s sister.
Relationships Involving the Terms ‘Grand’ and ‘Great’
- The relationships of the second generation are prefixed with the word Grand.
- Similarly, for a person, the first generation above him would be that of his/her parents (Father/ Mother). The next/second generation above him/her would be the parents of the parents who would be called Grand Parents/ Grand Father/ Grand Mother of that person. The next/ third generation parents would be called Great Grand Parents/ Great Grand Father/ Great Grand Mother of that person.
- This also applies to the collateral relationships.
For example Son of nephew of a person is called Grand Nephew; Brother of Grand Father is called Grand Uncle and so on.
- The fourth generation relationships are called Great Great Grand. For example, Son of Great Grand Son is Great Great Grand Son.
- There are two ways Martha could have a stepsister:
- a) If Martha’s mother marries second time, and her new husband (Martha’s new stepfather) already has a daughter from a previous marriage, that daughter is Martha’s stepsister because one of her parents is married to one of Martha’s parents.
- b) If Martha’s father marries second time, and his new wife already has a daughter, that daughter is again Martha’s stepsister.
Summary of Some Common Relationships
- Summary of some common Relationships is given below in tabular forms:
Logical Arrangement of Words
- Logical Arrangement is the meaningful arrangement of words in accordance with the natural laws and universally accepted concepts.
Different types of questions are covered in this chapter are as follows.
- Sequence of Occurrence of Events or Various Stages in a Process
- Sequence of Objects in a Class or Group
- Sequence in Ascending or Descending Order
- Sequential Order of Words According to Dictionary
In this type of problems, a sequence is to be formed with the given number of words in such a way that the particular arrangement of the words gives a logical step by step completion of some process or activity. In these questions, four/five/six words are given which are related to each other in some or other way. The candidate is required to find out the proper logical arrangement of these words from the given alternatives.
Type 1: Sequence of Occurrence of Events or Various Stages in a Process
- The given words may be such that they are related to a particular event or represent the various stages of a certain chained process from beginning to end.
- A candidate is required to choose that option from the given alternatives, which represents the correct logical sequence of the process.
Ex 1: Arrange the following words in a meaningful order
(a) 1, 3, 4,2
(b) 2, 3, 4, 1
(c) 3, 1, 2, 4
(d) 3, 2, 4, 1
The given words represent the various stages in the process of publishing. Firstly, the matter is written, followed by composition of that written matter. Then, this composed matter is printed followed by reading. So, the correct order is 3241.
Ex 2: Arrange the following words in a logical sequence.
(a) 1, 2, 3, 5, 4
(b) 5, 1, 3, 4, 2
(c) 5, 3, 1, 4, 2
(d) 4, 5, 1, 2, 3
For a job,
- Advertisement is the 1st stage
- Application is the 2nd stage
- Selection is the final stage
- Interview is the 4th stage
- Exam is the 3rd stage
Correct sequence = 5, 1,3, 4, 2
Type 2: Sequence of Objects in a Class or Group (From Part to Whole)
- Sometimes words may be given such that they are related to a particular class or a group. A candidate is required to choose that option from the given alternative which shows the correct logical sequence of the objects in a particular class or group. The examples given below will give you a better idea about such words.
Ex 3: Arrange the following words in a meaningful order.
(a) 3, 1, 2, 4, 5
(b) 3, 1, 2, 5, 4
(c) 3, 1, 4, 2, 5
(d) 3, 1, 4, 5, 2
The arrangement takes place according to the following logic:
The smallest unit amongst the five is member -
- A member is a part of family
- A family is a part of a community
- Community is a part of a locality
- Locality lies within a country
Correct arrangement = 3, 1, 2, 4, 5
Ex 4: Arrange the following words in a meaningful order.
1. Andhra Pradesh
(a) 3, 1, 4, 5, 2
(b) 1, 3, 5, 4, 2
(c) 3, 1, 5, 4, 2
(d) 3, 1, 2, 4, 5
Tirupati is a city situated in the Andhra Pradesh state of India. India is a part of the world and world in turn, is a part of the universe. So, the correct sequence of part to whole is given as Tirupati Andhra Pradesh India World Universe And the correct option showing the sequence is (c).
Type 3: Sequence in Ascending or Descending Order
- The items or objects represented by the given words may be related to each other in terms of their properties.
- A candidate is required to arrange the given words on the basis of increasing/ decreasing order of their size, age, need, value, intensity etc.
The examples given below will give you a better idea about such words
Ex 5: Arrange the following words in a logical sequence.
(a) 2, 4, 3, 5, 1
(b) 3, 2, 1, 5, 4
(c) 4, 5, 1, 3, 2
(d) 5, 4, 3, 2, 1
All the given words represent substances which can be arranged in the increasing order of their cost. The least costly is sand after which comes the cost of iron, followed by gold, diamond and the costliest among all is platinum. So, they can be arranged in a logical order as 3 2154.
Ex 6: Arrange the following words in a logical sequence.
(a) 1, 2, 4, 3, 5
(b) 1, 5, 3, 2, 4
(c) 4, 2, 3, 5, 1
(d) 4, 2, 5, 3, 1
All the words represent the counting numbers and their increasing order is given as below
Hundred Thousand Million Billion Trillion. This order is given in Option (d).
Type 4: Sequence Order of Words According to Dictionary
- In such type of question, the candidate is required to choose that option from the given alternatives, which is having the correct sequential order of words according to the English dictionary.
- To check the order of words in English dictionary, first of all check the first letter of each word to find which among these comes first English alphabet followed by second letter and so on.
- The word whose letter comes first in English alphabet comes, the word whose letter comes second in English alphabet comes second and so on.
Ex 7: Arrange the following words according to English dictionary.
(a) 2, 3, 1, 4
(b) 4, 2, 1, 3
(c) 4, 1, 3, 2
(d) 3, 1, 4, 2
According to the English dictionary, Chitin comes first, followed by Cholera which in turn is followed by Hepatitis and the last will be peptidoglycan. So, the correct sequential order of words is 4213.
- The Reasoning section of every competitive exam includes questions from the topic “Alphabet Test”. This topic is considered to be quiet important and every year a good number of questions are asked from this topic. We are providing you with Basic Concepts & Tricks to Alphabet Test related Questions in Reasoning which will surely help you in the upcoming SSC and other competitive Exams.
Basic Concepts & Tricks to Alphabet Test
- In this type, the question asked are based on finding the place of an English letter to the left or right of another English letter in the alphabetical order.
- Sometimes the Question is based on finding the number of English letter(s) between two different English letters.This type of question varies on the arrangement of alphabetical order.
- It can be Backward, first half backward, second half backward, multiple letter segments in changed order etc.
- Some of the questions asked are based on finding the middle letter of two specified letters and in some questions it is asked that which letters do not change their place after alphabet arrangement.
So, the detailed explanation with examples is as follow:
Place of the letter in forward order
- In this type of questions the exact letter has to be found out with the help of direction of place given in the question. The example discussed as below will give you a better idea about this type of questions.
Ex 1: Find the 11th letter to the left of 20th letter from left in the English alphabet.
(a) D (b) J
(c) K (d) I
- Let us see
- Hence, 11th letter to the left of 20th letter from left is I.
- In English alphabet 11th letter to the left of 20th letter of your left =(20-11) th letter from the left=9th letter from the left =I
Place Of Letter in Completely Backward Order
- In such questions the order of letters is completely reversed or they are counted from Z to A and then the place of letter is asked with the help of direction.
Ex 2: If English alphabet is written in backward order, then what will be 13th letter to the left of the 3rd letter from right?
- The backward order is written as
Now, the 13th letter to left of the 3rd letter from right is P.
In backward order of alphabet,13th letter to the left of the 3rd letter of your right =(3+13)th letter from right =16th letter from right P.
Place of a Letter When First Half is in Backward Order
- In such type of question, only the 1st half of the order of alphabetical series is reversed and remaining are left unaltered i.e., order of A to M is reversed and then questions related to position of latter are asked.
Ex 3: If 1st half of the English alphabet is written in backward order, then what will be the 7th letter to the left the 10th letter from your right?
Let us see
The 7th letter to the left of 10th letter from our right is D.
Place of a Letter When Second Half is in Backward Order
In such type of questions the 2nd half is reversed i.e., from N to Z and remaining are kept as it is and then questions related to place of English alphabet are asked.
Ex 4: If 2nd half of the English alphabet is written in backward order, then what will be the 7th letter to the right of 13th letter from your left?
- Let us see
The 7th letter to the right of 13th letter from our left is T.
Middle Letter between Two letters
- In these types of questions, it is asked to find the middle letter the two specified letters of English alphabet.
Ex 7: Which letter is in the middle of 7th letter from left and 10th letter from right in the English alphabet?
Let us see
Letters between G and Q is L.
- 10th letter from right =27-10 =17th letter from left.
- Required middle letter =7+(17-7)/2 =24/2 =12th letter from left =L
Same Position of Alphabet after Arranging Alphabetically
- In this type of questions, a word is given and then asked how many letters remain same in their position, if they are arranged in alphabetical order.
Ex 8: How many such letters are there in the word ‘CADMP’ which remain same in their position, if they are arranged in alphabetical order?
- So, such type of letters are D, M and P.
- Generally in Ranking Arrangement questions, position/rank of a person from left-right/top-bottom is given and and total number of persons is asked.
- There are several types of Ranking Arrangement and we are providing the methods to crack them.
- Total number of persons = (Sum of the number of same person from both sides) – 1
Example: In a row of persons, Position of Rahul from left side of the row is 34th and position of Rahul from right side is 37th. Find the total number of persons in the row ?
Sol: Total no. of person= (Position of Rahul from left + Position of Rahul from right) – 1 =(34 + 37)-1= 71-1=70
- Position of a person from other side= (Total number of persons- Position of the same person given side)+1
Example: In a row of 22 persons, Position of Rahul from right side of the row is 13th. Find the position of Rahul from left side of the row?
Sol: Position of Rahul from left=(Total number of persons- Position of Rahul from right side) +1 =(22-13)+1= 9+1= 10
- When the positions of two persons are given from both ends and the total number of persons are also given and we have to find the number of persons between them-
- There are two cases:-
- When there is no overlapping and we have to find the number of persons between them.
- No. of Persons between two different persons = Total no. of Persons – (Sum of positions of two different persons from both sides)
Example: In a row of 62 persons. Rahul is 24th from left side of the row and Nitesh is 20th form the right side of the row. Find out the number of persons sitting between them?
Sol: No. of Persons between Rahul and Nitesh= 62-(24+20)=62-44=18
- When there is overlapping and we have to find the number of persons between them.
- of Persons between two different persons = (Sum of positions of two different persons from both sides) -Total no. of Persons –2
Example: In a row of 62 persons. Rahul is 36th from left side of the row and Nitesh is 29th form the right side of the row. Find out the number of persons sitting between them?
Sol: No. of Persons between Rahul and Nitesh=(36+29)-62-2=65-62-2=1
- If total no. of Persons is to be asked and positions of different persons from any side are given then it is always a case of ‘cannot be determined’. Because we do not know if there will be overlapping or not.
Example: In a row Position of Rahul from left side of the row is 22nd and position of Nitesh from right side of the row is 35th. Find the total no. of students in the row?
Solution: Cannot be determined
- If positions are interchanged.
Example: Rahul and Nitesh are standing in a row of persons. Rahul is 12th from left side and Nitesh is 18th from the right side of the row. If they interchanged their positions Rahul becomes 25th from left. Find these-
a) New position of Nitesh from right side
b) Total number of person
c) Number of person between them
Sol: A) Rahul Position changes from 12th to 25th from left end. So there is an increase of 13 ranks. Since Rahul and Nitesh both are interchanged their positions so there must be same increase in ranks. So new position of Nitesh from right side= 18 +13= 31
B) In this questions Rahul position changes from 12 to 25 from left. That means 24 persons are standing from his left side. Now Rahul is at Nitesh’s position which is 18th from the right side. That means 17 persons are standing from his right. Add all these left and right= 24+17+1(Rahul’s own)=42 total persons
C) of persons between Rahul & Nitesh = (Position of rahul from left after interchanging– Position of Rahul from left before interchanging) – 1 ⇒ No. of persons between Rahul & Nitesh = (25 – 12) – 1 = 13 – 1 = 12
If positions of two persons are given and third person are sitting exactly between them.
Example: In a row of persons, position of Rahul from left side of the row is 10th and position of Nitesh from right side of the row is 9th. If Gaurav is sitting just in middle of Rahul and Nitesh and position of Gaurav from left of the row is 16th. Find the total number of persons in the row?
Sol: Position of Gaurav from left is 16th and Rahul from left is 10th so there are (16-10-1=5) persons are sitting between Rahul and Nitesh . As Gaurav is sitting exactly middle between them so 5 persons sitting between Gaurav and Nitesh. Position of Gaurav from right= Position of Nitesh from right 9 + 5 +1= 9+6=15th
Total number of persons= Sum of Gaurav’s positions from both sides -1 =(16+15)-1=31-1=30
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