Question

Gyan Prakash left for his college in his car -
(J) He drove 15 km towards the North and then 10 km towards the West.
(K) He then turned South and covered 5 km.
(L) Further, he turned to the East and moved 8 km.
(M) Finally, he turned right and drove 10 km.
How far and in which direction is he from his starting point?

• A. 2 km West
• B. 5 km East
• C. 3 km North
• D. 6 km South

Hint:

Always draw a quick direction compass (N, S, E, W) on your rough sheet. Draw each movement vector proportionally to scale so you can visually verify your mathematical coordinates.

Answer 1

The Correct Option is A

Step 1: Set coordinates.
Start at $(0,0)$, with North as $+y$, South as $-y$, East as $+x$, West as $-x$.
Step 2: Apply step (J).
$15$ km North then $10$ km West moves him to $(-10,15)$.
Step 3: Apply step (K).
Turning South for $5$ km gives $(-10,10)$.
Step 4: Apply step (L).
Moving East $8$ km gives $(-2,10)$.
Step 5: Apply step (M).
He faces East, so a right turn points South; $10$ km South lands him at $(-2,0)$.
Step 6: Compare with start.
From $(0,0)$ to $(-2,0)$ is $2$ km along the negative-x axis, that is, West.
\[ \boxed{\text{2 km West}} \]