Rajan's Journey Directions
Rajan's path involves several segments with specified distances and 90-degree turns. To determine the return path to Point A, we calculate the net displacement from the start (A) to the end (P).
Position Calculation from A
We analyze the movements along the East-West and North-South axes separately.
East-West Position Calculation
Movements affecting the East-West position:
- First leg: 51 km East (+51 km).
- Third leg: 56 km West (-56 km).
- Fifth leg: 5 km West (-5 km).
The net East-West displacement from A to P is: \(51 \text{ km} - 56 \text{ km} - 5 \text{ km} = -10 \text{ km}\) This means Point P is 10 km West of the North-South line passing through A.
North-South Position Calculation
Movements affecting the North-South position:
- Second leg: 56 km South (-56 km).
- Fourth leg: 63 km North (+63 km).
The net North-South displacement from A to P is: \(-56 \text{ km} + 63 \text{ km} = +7 \text{ km}\) This means Point P is 7 km North of the East-West line passing through A.
Return to Point A Calculation
From the calculations, Point P is located 10 km West and 7 km North relative to Point A.
To return to Point A from Point P, Rajan must travel in the opposite directions:
- 10 km East (to cancel the 10 km West position).
- 7 km South (to cancel the 7 km North position).
The required movements are 10 km East and 7 km South. Option 3, "7 km to the south", matches the North-South component required for the return journey.
Similar Questions
- 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.)
- A taxi travels 7 km south, then turns towards the east and travels 5 km, then turns towards the north and travels 7 km and then turns to its left and travels 2 km. What is the location of the taxi now with respect to its starting position?
- Two fielders, I and J, start from the same point on a ground. I runs 20 m north and then turns towards the east and runs 35 m. He then turns to his right and runs 15 m. Meanwhile, J runs 30 m north and then turns right and runs 35 m. Where is J now with respect to I?
- A man walks 6 km towards north and turns left and walks 2 kms towards West. If he has started from point Z and reached point A, then what is the shortest distance between point Z and A.
- A village girl walks 3 km east starting from her home in search of water. She then turns south and walks 2 km, then she turns east and walks 7 km, then she turns to her left and walks 2 km. Where is her home with respect to her position now?
- Two village women M and N start walking from the same point. M walks 4 km west, then turns left and walks 2 km. Meanwhile N walks 6 km south, then turns west and walks 4 km, then turns left and walks 1 km. Where is N with respect to M?
- Two fielders, I and J, start from the same point on a ground. I runs 20 m north and then turns towards the east and runs 35 m. He then turns to his right and runs 15 m. Meanwhile, J runs 30 m north and then turns right and runs 35 m. Where is J now with respect to I?
A man starts from ‘O’, travels 20 km towards East to reach point ‘A’, turns right and travels 10 km to reach point ‘B’, turns right and travels 9 km to reach point ‘C’, turns right and travels 5 km to reach point ‘D’, turns left and travels 11 km and stops for some time and travels 1 km to reach point ‘E’ and then turns right and travels 6 km to reach point ‘F’.
What is the shortest distance between point ‘A’ and point ‘D’?In the morning X and Y are walking towards each other in a park. When they meet, Y's shadow' falls upon X. In which direction was X facing?
Two workers K and L start walking from the same point. K walks 5 km North, then turns right and walks 2 km. Meanwhile, L walks 3 km West, then turns South and walks 4 km. Finally L turns left and walks 5 km. Where is K with respect to L?
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.)
