## Directions Based Simple Problems

**Question 1**

Raju's school was exactly 1500 m to the east of his home. He used to walk to his school daily. He walked 200m towards east. Then he turned right and walked 100 m to reach his friend Ravi's house. From Ravi's house both walked 1300m towards east. Then they turned left and walked to reach the school. What is the total distance walked by Raju.

**Answer :** 1700m

By Plotting the path of Raju, we get the following diagram

The distance travelled by Raju to School = AB + BC + CD + DE = 200 + 100 + 1300 + 100 = 1700m

**Question 2**

Arul was going to market from his home. He walked 4 Km to the north, turned right and walked 3 Km. He then turned left and walked 4 Km. Then he took a left and walked till he reached the market which was exactly to the east of his house. Find the distance of the market from his home along north.

**Answer :** 8km

From the above diagram, the distance of the market from his home = AE = AB + BE = AC + CD = 4 + 4 = 8km

**Question 3**

Starting from his house, Rahul walked 5 Km to the north east to reach a shop. From there he took a right and walked another 5 Km to reach his friends house. How far is his friend's house from his house (along eastern direction)?

**Answer : **sqrt(50)

From the given information the path can be drawn as,

Since the path is in the form of right angled triangle, to find the distance we can apply pythagoras theorem,

AC^{2} = AB^{2} + BC^{2}

AC = sqrt(AB^{2} + BC^{2})

= sqrt(5^{2} + 5^{2})

= sqrt(50)

**Question 4**

Rajiv was jogging around a hemispherical park. How long he will jog to complete one lap if the radius of the park was 200m.

**Answer :** 200(2 + pi)

The total distance covered by him for one lap = diameter of hemisphere + 1/2 (circumference of hemisphere)

= 400 + 1/2 (2 x pi x r)

= 400 + 1/2 (2 x pi x 200)

= 400 + (pi x 200)

= 200 (2 + pi)