Directions

Note: 
1)There are 8 directions in all i.e. N, S, E, W, NE, SE, SW, NW
2)Angle between 2 crosses i.e. NW & NE or N and E etc is 90*
3)Angle between direction and a cross is 45* i.e. between N & NE or E and SE, etc.




Main Questions that are asked:
1)Find the Final Direction
2)Starting  point direction with respect to the ending point
3)Ending point direction with respect to starting point




Example 1.
A Person is walking towards east 5 meters then he turned towards his right and walks 10 meters. Later in the journey he turned towards his right direction and walks for 15 meters finally he turns right and walks 10 meters.

(i)What is his final direction?-ans:North

(ii)How far is he from his starting point and in which direction?- ans: 10 meters-west

(iii)In which direction is his starting point from ending point?-ans: East



 

SHORT CUT METHOD:
 

Steps:

1)The 1st line in the question says that person walks 5m east so write 5m under the east column.
2)The 2nd line says that he turns right and walks 10m since he is facing east so his right would be ‘SOUTH’ direction therefore he walks 10m south so write 10m under the south column
3)The 3rd line says that he turns right again and walks 15m so right of south is west so write 15m under west column
4)Further the question says that he finally turns right and walks 10m so right of west direction is north so write 10m under north column.
So answer is 10 meters west ( see table for the reason)
5 )LOGIC behind the short cut

 a) Same direction
   Ex.North
      10 m
      10 m = 20m
   Then it gets added



b) Opposite direction

 


3) Opposite direction
 



Note for step 3 : for point three take the direction asthe bigger one this becomes the starting point direction with respect to ending point therefore the ending direction with respect  to starting point is east.

6)Drawback though this is the fastest way of solving a direction without using a diagram. But we cannot find the ending   direction with this step.





Q.A person is walking towards south for 50 meters. Later he look left and walks30 m.Again he took left and walks  80m. later in the journey he took right and   walks for 10 meters finally he moves to his left and walks 30m and again takes 30m to his left.

 (i) His final direction? Ans:West
(ii) How far is he from his starting point and in which direction?






Q 1.A person is walking towards west for 25m later he turns left and walks 30 meters. Again he takes left and walks 50 meters. Later he takes left and walks 38 meters. Finally  he walks 21 meters to his left. How far is he from the starting point and in which direction?

 (1) 20 – SW
 (2) 80 – NE
 (3) 4√5-  NE
 (4) 5 – SW
 (5) None of the above



Learn the following table:






Q 2.Shiva is facing N, he turns 180* and 45* in clockwise direction and then 270* in anti-clockwise direction. Finally again turns 180*. What is this facing direction now?
 (1) SE
 (2) SW
 (3) South
 (4) North east
 (5) None of the above

Q 3.A lady runs 12 km towards north. Then 6 km towards south and 8 km towards east. How for is she from her starting point and in which direction?
 (1) NE – 20 km
  (2) NE – 15 km
 (3) NW – 10 km
 (4) NE – 10 km
 (5) None of the above

Q 4.Point ‘D’ is 14m to its west point of ‘A’.
   Point ‘B’ is  4m towards south of ‘D’.
   Point ‘F’ is  9m towards south of ‘D’.
   Point ‘E’ is 7m towards east of ‘B’
   Point ‘C’ is 4m towards north of ‘E’.
   Point ‘G’ is 4m towards south of ‘A’.

(I) Which of the following points are in straight line?
  (1) DEA
  (2) EGC
  (3) DBG
  (4) EGB
  (5) FBC

(II) Point A is in which direction with respect to ‘C’?
  (1) North
  (2) South
  (3) East
  (4) West
  (5) None of the above

(III) If a person walks 5m towards north from point ‘F’ and then takes a right turn and started  walking. Which of the following points would he reach.
  (1) G
  (2) D
  (3) E
  (4) A
  (5) C

(IV) Point D and C are in which direction of point G?
  (1) North East
  (2) West
  (3) North West
  (4) South West
  (5) None of the above


 Q 5. A+B means A is 10m ‘N’ of B
     A-B means A is 10m ‘S’ of B
     A*B means A is 5 m ‘E’ of B
     A@B means A is 15m ‘W’of B 


(I) In a code “P+O-R×S@T” is written, the point ‘P’ is in which direction of point T?
  (1) East
  (2) South
  (3) west
  (4) NW
  (5) None

(II) What is the distance between point ‘P’ and ‘S’ in the above expression?
  (1) 5m
   (2) 7m
  (3) 10m
  (4) 15m
  (5) None of the above

Q 6. Raju is walking towards west, be takes 3 turns while walking. All at a backward angle of 45* towards his right, right and left find in which direction is he facing now?
  (1) NS
   (2) East
  (3) West
  (4) NE
  (5) None of the above



SHADOWS CONCEPT:
If sun rises in the east shadow will be in the west (morning time)

If sun sets in the west shadow will be in the east Evening time i.e. after 12:00 PM)
At exactly 12:00 there is no shadow (mid noon of midnight)



 




Q 7. In the Evening time Rekha is walking on the ground If her shadow is towards right then what is the facing direction of Rekha?
(1) North
(2) South
(3) East
(4) West
(5) None of the above

Q 8.  In the morning time, 2 persons A and B are talking to each other, standing in a straight line in a ground. If A’s shadow direction is to the left of B. What is the face direction of B?
 (1) north
 (2) south
 (3) east
 (4) west
 (5) none



Answers:

1) 3
2) 1
3) 4
4) I) 4
    II) 3
   III) 3
   IV) 3
5) I) 3
    II) 1
6) 4
7) 1
8) 1


Order And Ranking concepts

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 :

1. 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

2. 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

3. 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  

4. 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

Inequality concepts

Inequalities concepts and its application:


(i) A > B ≥ C 
     > is common                
     A > C             

(ii) A ≥ B > C
     A > C

Table:












Answer Options:
(1) Only 1 is true
(2) If only 2 is true
(3) Either 1 or 2 true
(4) Neither 1 nor 2 is true
(5) Both 1 and 2 are true

Examples:

1) P > Q > R < S ≥ T
A) (i) P > R (T)
    (ii) R < P (T) - (5)

B) (i) P > S (F) 
    (ii) R > P (F) - (4)

C) (i) R = T (F) 
    (ii) R > T (F) - (4)

2) P < Q ≤ R < S > T > U≠Z


A) (i) P < S  

    (ii) Q ≤ S

B) (i) R > T  
    (ii) S > U

C) (i) S > Z  
    (ii) R > P

D) (i) P ≤R 
     (ii) Q ≤ S

E) (i) P > T  
    (ii) P ≤ S

F) (i) P = Z  
    (ii) U ≤ R

Answers:
A) (i) T  
    (ii) F  (1)
B) (i) F 
    (ii) T  (2)
C) (i) F 
    (ii) T  (2)
D) (i) F 
    (ii) F  (4)
E) (i) F 
    (ii) F  (4)
F) (i) F 
    (ii) F  (4)

3) M≤ N≤ O< P; K = L≥ O > C


A) (i) M < O  

     (ii) M ≤ P

B) (i) K ≥ N 
    (ii) M ≤ O

C) (i) P ≥ K  
    (ii) P ≤ M

D)  (i) M = C 
      (ii) N > C

E) (i) C > P  
    (ii) P = C

F) (i) D = O  
    (ii) D ≤ M

Answers:
A) (i) F 
    (ii) F-(4)
B) (i) T 
    (ii) T-(5)
C) (i) F  
    (ii) F-(4)
D) (i) F  
    (ii) F-(4)
E) (i) F  
    (ii) F-(4)
F) (i) F  
    (ii) F-(4)

4)T < P≤ U ;  L> U≤K ; P≥ R


A) (i) K≥ R 

     (ii) L> R

B) (i) L > U ≥ P 
    (ii) R ≤ U

C) (i) T < K  
    (ii) L > T

D) (i) R > L  
   (ii) R ≤ L

E) (i) U ≤ R  
   (ii) T < R

Answers:
A) (i) T 
    (ii) T (5)
B) (i) T  
    (ii) T (5)
C) (i) T 
    (ii) T (5)
D) (i) F 
    (ii) F (4)
E) (i) F 
    (ii) F (4)


5) A≥B≠ C≥ F ;  Z < C ≤ D < E 



A) (i) A ≥ B > C

    (ii) D ≥ C ≥ F

B)  (i) A > E  
     (ii) D < B

C) (i) B > C  
    (ii) B < D

4) (i) F > E  
   (ii) F < E

5) (i) B < C ≥ F
   (ii) E ≥ C > B

Answers:
A) (i) F 
    (ii) F (4)
B) (i) F 
    (ii) F (4)
C) (i) F 
    (ii) F (4)
D) (i) F 
    (ii) T (2)
E) (i) F  
    (ii) F (4)



Either or condition:


1)Subject and predicate of the 2 conclusions should be same 
(may not be in the same order) 


2)Individually both conclusions should be false 


3)Both conclusions should cover maximum solutions 
according to the given statement. 


5)A ≥ B≥ C

A) (i) A > C 
    (ii) A = C

B) (i) C < A 
    (ii) C = A

C) (i) C ≠ A 
    (ii) A = C

D) (i) A > C 
    (ii) A < C

E) (i) A > C 
    (ii) A ≤ C

Answers:
A) (i) F  
    (ii) F (3)
2) (i) F  
    (ii) F (3)
3) (i) F  
    (ii) F (4)
4) (i) F  
   (ii) F (4)
5) (i) F  
    (ii) F (4)

Exceptions to Either Or

6) P > Q > R < S

 A) (i) P≤ S 
     (ii) P≥ S

B) (i) P ≠ S 
    (ii) S = P

C) (i) U ≤ V
    (ii) U ≥ V

D) (i) S>P
    (ii) S≤P

E) (i) P≠ T (> ,<) 
    (ii) P = T

F) (i) U≤ V
    (ii) V ≥ U

G) (i) P ≤ T
    (ii) P ≥ R

H) (i) P ≤ T
    (ii) P > R

Note: Even though T is not there in the statement, but if there is no definite relation 
between the ‘2’ letters and covers 3 maximum relations, then it is not false.
Answers:
A) (i) F  
    (ii) F (3)
B) (i) F  
    (ii) F (3)
C) (i) F  
    (ii) F (3)
D) (i) F  
  v (ii) F (3)
E) (i) F  
    (ii) F (3)
F) (i) F  
    (ii) F (4)
G) (i) F  
    (ii) F (4)
H) (i) F  
    (ii) T (2)