Prakash starts from Point A and drives 37 km towards the north. He then takes a left turn, drives 40 km, turns left and drives 55 km. He then takes a left turn and drives 64 km. He takes a final left turn, drives 18 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-degree turns only unless specified.)
24 km to the west
Place Point A at the origin and track each move as a coordinate change, with north as +y and east as +x.
Start at A(0, 0); drive 37 km north to reach (0, 37).
A left turn while facing north points him west; driving 40 km gives (-40, 37).
A left turn while facing west points him south; driving 55 km gives (-40, -18).
A left turn while facing south points him east; driving 64 km gives (24, -18).
A left turn while facing east points him north; driving 18 km gives P(24, 0).
Point P(24, 0) and Point A(0, 0) lie on the same horizontal line, so the shortest distance is 24 km, and A is directly to the west of P.
Hence, he should drive 24 km to the west.
Similar Questions
Smita starts from Point A and drives 6 km towards north. She then takes a left turn, drives 8 km, turns left and drives 10 km. She then takes a left turn and drives 12 km. She takes a final left turn, drives 4 km and stops at Point B. How far (shortest distance) and towards which direction should she drive in order to reach Point A again? (All turns are 90 degrees turns only unless specified.)
Mr. Tosi starts from Point A and drives 18 km towards the East. He then takes a right turn, drives 13 km, turns right and drives 27 km. He then takes a right turn and drives 23 km. He takes a final right turn, drives 9 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-degree turns only unless specified.)
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Kiran starts from point B and drives 15 km towards South. He then takes a left turn, drives 8 km, turns right, and drives 5 km. He then takes a right turn and drives 8 km. Finally, he takes a right turn, drives 13 km, and stops at point P. How far (shortest distance) and towards which direction should he drive in order to reach point B again? (All turns are 90-degree turns only unless specified.)
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Mr. Samten starts from Point A and drives 15 km towards south. He then takes a left turn, drives 9 km, again turns left and drives 42 km. Next, he takes a left turn, drives 11 km, turns left and drives 17 km. He then takes a right turn and drives 10 km. He takes a final left turn, drives 10 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 degree turns only, unless specified.)
Ritwik starts from Point A and drives 23 km towards the east.
He then takes a right turn, drives 14 km, turns right and drives 26 km.
He then takes a right turn and drives 19 km.
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How far (shortest distance) and towards which direction should he drive in order to reach Point A again?
All turns are 90-degree turns only unless specified.
Kartik starts from Point A and drives 19 km towards the south. He then takes a left turn, drives 13 km, turns left and drives 24 km. He then takes a left turn and drives 22 km. He takes a final left turn, drives 5 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-degree turns only unless specified.)
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Important Questions from Direction and Distance Turns
After leaving school, Hemant and Anurag walk towards the north for 1 km to reach a bus stop. From the bus stop, Hemant turns left and walks for 500 m. Then he turns towards his left and walks for 2 km to reach his home. From the bus stop, Anurag turns right and walks for 250 m. Then he turns right and walks for 1 km to reach his home. In which direction is Anurag's home from Hemant's home?
A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?
A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?
Two friends Xand Ystart running and they run together for 50 m in the same direction and reach a point. Xturns right and runs 60 m, while Yturns left and runs 40 m. Then Xturns left and runs 50 m and stops, while Yturns right and runs 50 m and then stops. How far are the two friends from each other now?
Rohan walks 10 km towards north from a point A. Then he turns right and walks 6 km. Then, he again turns right and walks 10 km. In which direction is he now from the starting point?
