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Other different types of problem from Ordering and Ranking

Type – 3

Finding the mid number between two persons

To find the mid number of an order we need

(i) Rank of one person from one end

(ii) Rank of another person from other ends

(iii) Total number of persons in the order.

Formula:

(i) Mid number = Total Person – (Rank of one person from one end + Rank another person from other ends)

[When the total person is more than the addition of the rank of two person from two different ends.]

(ii) When the total person is less than the addition of the rank of two person from two different ends.

Mid Number = (Rank of one person from one end + Rank of another person from other end) - Total number – 2

Example – 1

In a row of 58 girls. Payel is 15th from the right end and Swarnali is 24th from the left end. Then find how many girls are there in between Payel and Swarnali?

a) 21                                                     

b) 19                                                     

c) 20

d) 18                                                     

e) None of these

Solution:

Payel is 15th from the right end.

Swarnali is 24th from the left end.

So, Rank of Payel and Swarnali from different end = (24 + 15) = 39

Total girls = 58

Total girls are more than the total rank of Payel and Swarnali from a different end.

So, girls in between Payel and Swarnali is (58 - 39) =19

So, option (b) is correct.

Example – 2

In a row of 35 boys, Souvik is 21st from the left end and Partha is 24th from the right end. Then find how many boys are in between Sovik and Partha.

a) 7                                                       

b) 6                                                      

c) 8

d) 5                                                      

e) None of these

Solution:

The rank of Souvik is 21st from the left end.

The rank of Partha is 24th from the right end.

So, the total rank of Souvik and Partha from the different end is (24 + 21) = 45

The total numbers of boys are 35

So, the total number of boys is less than the total rank of Souvik and Partha from different ends.

So, there are 45 – 35 – 2 = 8 boys in between Souvik and Partha.

So, option (c) is correct.

Type – 4

Finding the total number of persons when value is given is

(i) Mid number between 2 persons

(ii) Rank of one person from one end

(iii) Rank of another person from another end

Formula

(i) Total number = Mid Number + Rank of one person + Rank of another person from other ends.

This is the maximum total numbers of person and simple case

(ii) Total number = (Rank of one person from one end + Rank of another person from another end) – (Mid number  + 2)

This is the minimum total number of person and this is for an overlapping case.

Example:

In a row of women, Riya is 14th from the right end and Ani is 26th from the left end. There are 6 women sitting in between Riya and Ani. Then find the total number of women

a) 46                                                     

b) 32                                                     

c) 40

d) 45                                                     

e) Either 32 or 46

Solution:

If Riya and Ani does not overlap then the total number of women is (6 + 14 + 26) = 46

And If Riya and Ani overlap each other then total number of women is (14 + 26) - (6 + 2) = 32

So, the total number of women is either 46 or 32.

So, option (e) is right.

Type – 5

Finding the exact mid-position between two person

Example

In a row of 48 men, Saikat is 14th from the end and Suraj is 21st from the left end. Rocky is sitting exactly between Saikat and Suraj then what is the rank of Rocky from the left end?

a) 29th                                                   

b) 21st                                                   

c) 27th

d) 28th                                                   

e) None of these

Solution:

Total Rank of Saikat and Suraj from different end is (21 + 14) = 35

Total men = 48

So, Total men between Saikat and Suraj = (48 – 35) = 13

∴ Position of rocky is (14 + 7)th = 21st from left end.

So, option (b) is correct.

Note: If Mid number between two persons is even. Then we cannot determine the exact mid position.

Type – 6

Based on Interchange of Rank

In a row, Amit is 24th from the left end and Ashish is 27th from the right end. When they interchange their position respectively. Then Amit becomes 29th from the right end. Then what will be A’s position from the left end after interchanging?

a) 21                                                     

b) 23                                                     

c) 24

d) 22                                                     

e) None of these

Solution: 

Total no. Of persons 

= Rank of Amit left end + Rank of Amit from after interchange – 1 

= 24 + 27 – 1 = 51 – 1 = 50

Ashish rank from left end after interchange will be = 50 – 29 + 1 = 21 + 1 = 22

So, option (d) will be correct.