**Formulas to determine the positioning of a person:**

1)Left + Right = Total + 1

2)Left = Total + 1 – Right

3)Right = 1 + 1 – left

**Note :** the above formulas are only for a single person’s position

**Example:**

3rd from left

3rd from right

Total= 3+3-1

**Same for vertical & Horizontal**

1)Total + 1 = top + Bottom

2)Top = Total + 1 – Bottom

3)Bottom = Total + 1 – Top

4)Total = Top + Bottom

Eg.1: In a row of 40 students, A is 13th from the left end, find the rank from right end.

**Ans **Total = 40

13L

A’s rank from right side = Total + 1 – left

= 40 – 13 + 1

= 27 + 1

= 28

**Eg2: M a row ‘P’ is 25th from left end, Q is 30th from right end. Find the total no. of students in all. **

**Ans.**

Cant be Determined as there are more than 1 possibilities

Case 1

**Note : **When total is not given and 2 persons positions from left and right are given, then answer is C.D

**Eg 3: In a row of children. A is 17th from left, B is 15th from right.**

(1) find the total number of children in the row

Ans. Can’t be determined, as there are more than 1 possibilities

**Eg 4: In a row of some children, S is 25th from left, T is 60th from right. If they interchanged their positions, then T becomes 70th from right end **

Find

(i) What is S’s right-hand position in new position

(ii) What is T’s left hand position in earlier position.

(iii) How many numbers of persons between S and T.

(iv) What is the total strength

(v) If ‘Q’ is placed exactly between S & T then what is his rank from left end?

**Answers **

1)S’s new position from left end = 35

2)T’s left hand position in earlier position = 35 L

i.e. L = 25 + 9 + 1

= 35

Or

L = 94 + 1 – R

= 95 – 60

= 35

3) Persons in between = 70 – 60 – 1

= 9

Or

Persons in between = Total – 25 – 60

= 94 – 25 – 60

= 94 – 85

= 9

4)Total strength = 25 + 60 + 9

= 95

Or

Total = 70 + 25 – 1

= 94

5)

**Ans :** 25 + 4 +1 = 30 from left

**Quiz** :

**In a group of 40 girls, when latha was shifted by 4 places towards her right, then she become 12th from the left end what was her earlier position from the right end of the row?**

1) 34

2) 32

3) 33

4) 35

5) none

**In a group of 40 boys, Raju is 12th from the left end and Raghu is 17th from the right end. If Dilip is placed exactly between them what is his right hand rank?**

1) 22

2) 23

3) 24

4) 25

5) none

**In a row of students, Ravi is 10th to left of Ramesh, who is 30th from the left end. If Ramesh is exactly in the middle of ravi and Sandeep, then find.**

**(I) How many minimum numbers of students is possible in that row? **

(1)39

(2)38

(3)40

(4)41

(5)Can’t be determined

**(II) What is the total strength? **

(1)90

(2)80

(3)40

(4)70

(5)Can’t be determined

**Amit is 24th from the left end and 6th from the right of Sumit. Anuj is 33th from the right end. Sumit is between Amit and Anuj.**

**(I) What will be the total strength?**

(1) 45

(2) 44

(3) 50

(4) 43

(5) None

**(II) What is Anuj’s position from the left end? **

(1) 11

(2) 10

(3) 12

(4) 13

(5) None

*Answers *

*1) 3*

*2) 2*

*3)I) 3*

* II) 5*

*4) I) 2*

* ii) 3*

**Explanation**

Members in between

24 – 12 – 1 = 11

Or

29 – 17 – 1 = 11

Why we subtract 1 is because we do not want to consider the 29th rank, we want the nos. between 29 & 17.

Dilip’s rank from right = 17 + 5 + 1 = 23