One day Prakash left home and walked 10 km towards south, turned right and walked 5 km, turned right and walked 10 km and turned left and walked 10 km. How many km will he have to walk to reach his home straight?
15
Direction problems are best handled by tracking position step by step, remembering that a right or left turn is judged relative to the direction currently being faced.
Take home as the origin. Prakash first walks 10 km south, so he is 10 km south of home, facing south.
He turns right. Facing south, the right hand points west, so he walks 5 km west. He is now 10 km south and 5 km west of home, facing west.
He turns right again. Facing west, the right hand points north, so he walks 10 km north. This exactly cancels the first southward leg, bringing him back to the latitude of home, 5 km west of it, facing north.
He turns left. Facing north, the left hand points west, so he walks a further 10 km west. He is now 15 km west of home and level with it.
Since he is due west of home with no north-south displacement remaining, the straight distance back is simply 5 + 10 = 15 km.
The key step is the second right turn, which undoes the southward movement entirely; a candidate who misses that cancellation would be left computing a diagonal.
Hence he will have to walk 15 km to reach home straight.
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Important Questions from Direction and Distance
- Johny starts from Point A and drives 6 km towards the North. He then takes a right turn, drives 17 km, turns right and drives 13 km. He then takes a right turn and drives 8 km. He takes a final right turn, drives 7 km and stops at Point P. How far (shortest distance) and towards which direction should he drive to reach Point A again? (All turns are 90 degrees turns only unless specified.)
- Town Q is to the east of Town P. Town R is to the south of Town Q. Town S is to the east of Town R. Town T is to the south of Town S. Town U is to the east of Town T. What is the position of Town U with respect to Town Q?
- Binoy starts from Point Y and drives 16 km towards the north. He then takes a right turn and drives 43 km, then turns right and drives 38 km. He then takes a right turn and drives 19 km. He takes a final right turn, drives 22 km and stops at Point Z. How far (shortest distance) and in which direction should he drive in order to reach Point Y again? (All turns are 90-degree turns only unless specified.)
- Himank starts from Point A and drives 13 km towards West. He then takes a left turn, drives 3 km, turns left and drives 16 km. He then takes a left turn and drives 6 km. He takes a final left turn, drives 3 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90° turns only unless specified.)
- Shyam starts from Point A and drives 12 km towards east. He then takes a right turn,
drives 7 km, turns right and drives 5 km. He then takes a left turn and drives 9 km. He
takes a final right turn, drives 7 km and stops at Point P. How far (shortest distance) and
towards which direction should he drive in order to reach Point A again? (All turns are
$90^{\circ}$ turns only unless specified.)
