Amit starts from Point Y and drives 14 km towards South. He then turns left and drives 35 km, takes a left and drives 68 km. He t…

Question

Amit starts from Point Y and drives 14 km towards South. He then turns left and drives 35 km, takes a left and drives 68 km. He then takes a left turn and drives 41 km. He takes a left turn, drives 54 km, turns right and drives 53 km to stop at Point Z. How far (shortest distance) and towards which direction should he drive in order to reach Point Y again? (All turns are 90° turns only unless specified.)

1. A. 57 km towards east
2. B. 56 km towards west
3. C. 61 km towards west
4. D. 59 km towards east (Correct answer)

Correct Answer

Option D — 59 km towards east

Detailed Solution & Explanation

The correct answer is 59 km towards east.

Key Points

• Track the position as coordinates, taking Y as the origin with east positive on the x-axis and north positive on the y-axis. Each "left" turn rotates the facing anticlockwise.
  • 14 km South → $(0,\,-14)$, now facing South
  • left (→ East) 35 km → $(35,\,-14)$
  • left (→ North) 68 km → $(35,\,54)$
  • left (→ West) 41 km → $(-6,\,54)$
  • left (→ South) 54 km → $(-6,\,0)$
  • right (→ West) 53 km → $(-59,\,0)$
• Point Z is at $(-59, 0)$ and Y at the origin. They share the same y-coordinate, so the return journey is due east, a distance of 59 km.

Additional Information

• Coordinates beat sketching in multi-turn direction problems. A diagram drawn to no scale quickly becomes unreliable after five or six legs, whereas the arithmetic cannot drift.
• Track the facing direction separately from position, and apply turns to it: facing South, a left turn gives East; facing North, a left turn gives West. Getting the turn convention wrong is the single commonest error.
• The vertical legs here cancel exactly — $-14 + 68 - 54 = 0$ — which is what puts Z level with Y and makes the final answer purely horizontal.
• Where the coordinates differ in both axes, the shortest distance is the straight line $\sqrt{(\Delta x)^2 + (\Delta y)^2}$, usually engineered to give a Pythagorean triple.