**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