Tanmay starts from Point Y and drives 23 km towards West. He then takes a right turn, drives 63 km, turns right and drives 31 km. He then takes a right turn and drives 27 km. He takes a right turn, drives 79 km. He then turns left, drives 36 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.)
71 km towards east
Starting facing West and turning right each time (West to North to East to South to West), the path covers 23 km West, 63 km North, 31 km East, 27 km South, and 79 km West, reaching coordinates (-71, 36) from Y at the origin.
The final left turn (from West to South) followed by 36 km South brings point Z to coordinates (-71, 0).
Since Y is at the origin (0, 0) and Z shares the same y-coordinate, only a horizontal move is needed: 71 km East from Z reaches Y.
Hence, Tanmay should drive 71 km towards the east to reach Point Y again.
Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?
Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 ° anticlockwise. Then she turns 45 ° clockwise, followed by a 135 ° anticlockwise turn. In which direction is she facing now?
Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?
At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?