Question : Directions: A man starts the journey from home. He goes 5 km to the north, then proceeds 10 km to the right. From there he again turns right and goes 10 km. How far is he from home?
Option 1: $\sqrt{200}$
Option 2: $\sqrt{150}$
Option 3: $\sqrt{225}$
Option 4: $\sqrt{125}$
Correct Answer: $\sqrt{125}$
Solution : Firstly, we will draw the diagram as per the given instructions –
In the above figure, A is the starting point and E is the finishing point of the man. AE is the distance between the man and his home. Here, BC = AD = 10 km; AB = DC = 5 km; DE = 10 – 5 = 5 km By applying the Pythagoras theorem – (AE)2 = (AD)2 + (DE)2 (AE)2 = (10)2 + (5)2 (AE)2 = 100 + 25 ⇒ AE = $\sqrt{125}$ km
So, the distance between the man and his home is $\sqrt{125}$ km. Hence, the fourth option is correct.
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Question : Directions: A man starts from a point, moves 9 km south, then turns east and goes 3 km. He turns south and walks 3 km, and then moves 8 km towards the west. How far is he from the starting point?
Option 1: 15 km
Option 2: 12 km
Option 3: 11 km
Option 4: 13 km
Question : Directions: A man goes 10 km westward, then turns right and proceeds 4 km, then travels 10 km towards left, then travels 8 km towards left, and finally goes 4 km northward. Calculate his distance from his initial place in the horizontal direction.
Option 1: 20 km
Option 2: 22 km
Option 3: 23 km
Option 4: 25 km
Question : Directions: Ruhi travels 10 km towards the north then turns left and travels 4 km and then again turns right and covers another 5 km and turns right and travels another 4 km. How far is she from the starting point?
Option 1: 5 km
Option 2: 10 km
Option 3: 15 km
Option 4: 20 km
Question : Directions: A person starts delivering letters 3 km southwards and then turns right. He covers 4 km on this road and again turns right. He delivers letters for 3 km and completes his daily beat. Then he turns left for lunch at home which is 5 km away. How far does he have to travel to reach the post office after lunch?
Option 3: 9 km
Option 4: 8 km
Question : Directions: Stanley starts cycling from Point A. He cycles x km towards the east and then turns right and cycles 3 km. He again turns right and cycles for (x + 1) km. He again turns right and cycles for (2x + 1) km. He takes a final right turn and cycles for 1 km to stop at Point B. Point B is 6 km north of Point A. What is the value of x?
Option 1: 9
Option 2: 3
Option 3: 4
Option 4: 5
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