Manoj walks a distance of 5 meters towards North, then he turns to east and walks a distance of 10 meters. Then he turns to his right and covers a distance of 15 meters. He then turns to his left and covers a distance of 15 meters. Which direction is he facing now?
Step 1: Manoj walks 5 m North, then turns to face East and walks 10 m.
Step 2: Facing East, he turns to his right, which points him South, and walks 15 m.
Step 3: Facing South, he turns to his left, which points him back East, and walks a final 15 m.
Step 4: His last movement was made while facing East, so that is his final direction: East.
Was this answer helpful?
0
Show Solution
Approach Solution -2
Rather than tracking every heading, the two turns after the initial North-to-East change can be looked at as a pair: a right turn followed later by a left turn cancel each other out and return Manoj to the heading he had right before the first of that pair. He was facing East just before the right turn, so after the right turn (now South) and the subsequent left turn, he is back to facing East, regardless of how far he walks in between.
North: North only ever describes the direction of his very first leg, since the turn to East happens immediately after, North cannot be his final heading.
East: East is the heading he held right before the right-left turn pair, and since a right turn followed by a left turn cancels out, he returns to facing East once both turns are complete.
West: reaching a West heading would require an odd overall combination of turns relative to his East-facing start, but a right-then-left pair is a net-zero change, so West is not the result.
South: South is only the direction he faced in the middle of the right-left pair, before the cancelling left turn brought him back to East.
