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Direction Sense

Distance and final direction after a set of moves.

45 solved questions · 15 easy · 20 medium · 10 hard

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Shortcuts & formulas

  • Directions in order clockwise: N, NE, E, SE, S, SW, W, NW. Right turn goes forward in this order, left turn goes back.
  • Shortest distance = Pythagoras on net north-south and net east-west displacement: d = sqrt(x^2 + y^2).
  • Common triplets: (3,4,5), (5,12,13), (8,15,17), (7,24,25) and their multiples.
  • Morning: the sun is in the east, so shadows fall west. Evening: the sun is in the west, so shadows fall east.
  • Facing the sun in the morning means facing east; then right = south, left = north.
  • To find the direction of the start from the end, reverse the direction of the end from the start.
  • Draw a small coordinate grid (east = +x, north = +y) and mark each leg; do not solve in your head.

Solved examples

Try each one first, then open the answer and the step-by-step solution.

Easy questions

Q1.

Rahul starts walking 5 km towards north. Then Rahul turns right and walks 4 km. Then Rahul turns right and walks 5 km. In which direction is Rahul now with respect to the starting point?

  1. AEast
  2. BWest
  3. CSouth
  4. DNorth
Show answer & solution

Answer: A. East

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 5 km north -> (0, 5) Leg 2: turn right, walk 4 km east -> (4, 5) Leg 3: turn right, walk 5 km south -> (4, 0) The end point is 4 km east and 0 km south of the start, i.e. towards East. Answer: East

Shortcut: Net east-west and net north-south displacement decide the direction; equal amounts give a diagonal.

Q2.

Sneha starts walking 2 km towards north. Then Sneha turns left and walks 4 km. Then Sneha turns right and walks 2 km. In which direction is Sneha now with respect to the starting point?

  1. ASouth-East
  2. BNorth-East
  3. CSouth-West
  4. DNorth-West
Show answer & solution

Answer: D. North-West

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 2 km north -> (0, 2) Leg 2: turn left, walk 4 km west -> (-4, 2) Leg 3: turn right, walk 2 km north -> (-4, 4) The end point is 4 km west and 4 km north of the start, i.e. towards North-West. Answer: North-West

Shortcut: Net east-west and net north-south displacement decide the direction; equal amounts give a diagonal.

Q3.

Vikram starts walking 2 km towards south. Then Vikram turns right and walks 4 km. Then Vikram turns left and walks 2 km. In which direction is Vikram now with respect to the starting point?

  1. ANorth-East
  2. BNorth-West
  3. CSouth-East
  4. DSouth-West
Show answer & solution

Answer: D. South-West

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 2 km south -> (0, -2) Leg 2: turn right, walk 4 km west -> (-4, -2) Leg 3: turn left, walk 2 km south -> (-4, -4) The end point is 4 km west and 4 km south of the start, i.e. towards South-West. Answer: South-West

Shortcut: Net east-west and net north-south displacement decide the direction; equal amounts give a diagonal.

Q4.

Meena is facing west. Meena turns 90° to the right. In which direction is Meena facing now?

  1. ASouth
  2. BEast
  3. CNorth
  4. DWest
Show answer & solution

Answer: C. North

Solution

Start: facing West. Turning right adds the angle clockwise and turning left subtracts it. turn 90 degrees right -> facing North Answer: North

Shortcut: Clockwise order: N, NE, E, SE, S, SW, W, NW. Right turn moves forward in this list, left turn moves back.

Q5.

Kiran is facing west. Kiran turns 90° to the left, then 90° to the left. In which direction is Kiran facing now?

  1. AWest
  2. BEast
  3. CSouth
  4. DNorth
Show answer & solution

Answer: B. East

Solution

Start: facing West. Turning right adds the angle clockwise and turning left subtracts it. turn 90 degrees left -> facing South turn 90 degrees left -> facing East Answer: East

Shortcut: Clockwise order: N, NE, E, SE, S, SW, W, NW. Right turn moves forward in this list, left turn moves back.

Q6.

Suresh is facing west. Suresh turns 90° to the right, then 180° to the right. In which direction is Suresh facing now?

  1. ANorth
  2. BSouth
  3. CWest
  4. DEast
Show answer & solution

Answer: B. South

Solution

Start: facing West. Turning right adds the angle clockwise and turning left subtracts it. turn 90 degrees right -> facing North turn 180 degrees right -> facing South Answer: South

Shortcut: Clockwise order: N, NE, E, SE, S, SW, W, NW. Right turn moves forward in this list, left turn moves back.

Q7.

Neha is facing west. Neha turns 90° to the right, then 90° to the left, then 90° to the right. In which direction is Neha facing now?

  1. ANorth
  2. BSouth
  3. CEast
  4. DWest
Show answer & solution

Answer: A. North

Solution

Start: facing West. Turning right adds the angle clockwise and turning left subtracts it. turn 90 degrees right -> facing North turn 90 degrees left -> facing West turn 90 degrees right -> facing North Answer: North

Shortcut: Clockwise order: N, NE, E, SE, S, SW, W, NW. Right turn moves forward in this list, left turn moves back.

Q8.

Arjun is facing south. Arjun turns 180° to the right, then 90° to the left. In which direction is Arjun facing now?

  1. AEast
  2. BNorth
  3. CSouth
  4. DWest
Show answer & solution

Answer: D. West

Solution

Start: facing South. Turning right adds the angle clockwise and turning left subtracts it. turn 180 degrees right -> facing North turn 90 degrees left -> facing West Answer: West

Shortcut: Clockwise order: N, NE, E, SE, S, SW, W, NW. Right turn moves forward in this list, left turn moves back.

Q9.

One morning just after sunrise, Priya was standing facing a pole. The shadow of the pole fell exactly to the right of Priya. Which direction was Priya facing?

  1. ANorth
  2. BSouth
  3. CEast
  4. DWest
Show answer & solution

Answer: B. South

Solution

The sun is in the east just after sunrise, so the shadow falls towards the west. The shadow is right of Priya's facing direction, so west is right of the facing direction. The direction to the right of South is west. Answer: South

Shortcut: Morning shadow points west, evening shadow points east (sun is opposite to the shadow).

Q10.

One evening just before sunset, Rahul was standing facing a pole. The shadow of the pole fell exactly to the left of Rahul. Which direction was Rahul facing?

  1. ASouth
  2. BNorth
  3. CEast
  4. DWest
Show answer & solution

Answer: A. South

Solution

The sun is in the west just before sunset, so the shadow falls towards the east. The shadow is left of Rahul's facing direction, so east is left of the facing direction. The direction to the left of South is east. Answer: South

Shortcut: Morning shadow points west, evening shadow points east (sun is opposite to the shadow).

Q11.

One morning just after sunrise, Sneha was standing facing a pole. The shadow of the pole fell exactly in front of Sneha. Which direction was Sneha facing?

  1. ANorth
  2. BEast
  3. CSouth
  4. DWest
Show answer & solution

Answer: D. West

Solution

The sun is in the east just after sunrise, so the shadow falls towards the west. The shadow is front of Sneha's facing direction, so west is front of the facing direction. So Sneha faces west. Answer: West

Shortcut: Morning shadow points west, evening shadow points east (sun is opposite to the shadow).

Q12.

B is 4 m to the east of A. In which direction is B with respect to A?

  1. AWest
  2. BEast
  3. CSouth
  4. DNorth
Show answer & solution

Answer: B. East

Solution

Take A as (0,0). B is 4 m east of A -> (4, 0) So B lies due east of A. Answer: East

Shortcut: Mark each position on a quick grid; equal east-west and north-south offsets give a diagonal direction.

Q13.

Q is 6 m to the north of P. R is 6 m to the west of Q. In which direction is R with respect to P?

  1. ANorth-West
  2. BSouth-East
  3. CNorth-East
  4. DSouth-West
Show answer & solution

Answer: A. North-West

Solution

Take P as (0,0). Q is 6 m north of P -> (0, 6) R is 6 m west of Q -> (-6, 6) So R is 6 m west and 6 m north of P, i.e. towards North-West. Answer: North-West

Shortcut: Mark each position on a quick grid; equal east-west and north-south offsets give a diagonal direction.

Q14.

A temple is 6 m to the south of a house. A school is 6 m to the east of a temple. In which direction is a school with respect to a house?

  1. ASouth-East
  2. BNorth-West
  3. CSouth-West
  4. DNorth-East
Show answer & solution

Answer: A. South-East

Solution

Take a house as (0,0). a temple is 6 m south of a house -> (0, -6) a school is 6 m east of a temple -> (6, -6) So a school is 6 m east and 6 m south of a house, i.e. towards South-East. Answer: South-East

Shortcut: Mark each position on a quick grid; equal east-west and north-south offsets give a diagonal direction.

Q15.

Y is 2 m to the east of X. Z is 2 m to the south of Y. In which direction is Z with respect to X?

  1. ANorth-West
  2. BSouth-West
  3. CNorth-East
  4. DSouth-East
Show answer & solution

Answer: D. South-East

Solution

Take X as (0,0). Y is 2 m east of X -> (2, 0) Z is 2 m south of Y -> (2, -2) So Z is 2 m east and 2 m south of X, i.e. towards South-East. Answer: South-East

Shortcut: Mark each position on a quick grid; equal east-west and north-south offsets give a diagonal direction.

Medium questions

Q16.

Ravi starts walking 6 km towards east. Then Ravi turns right and walks 9 km. Then Ravi turns left and walks 6 km. How far is Ravi from the starting point (straight-line distance)?

  1. A15 km
  2. B21 km
  3. C12 km
  4. D17 km
Show answer & solution

Answer: A. 15 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 6 km east -> (6, 0) Leg 2: turn right, walk 9 km south -> (6, -9) Leg 3: turn left, walk 6 km east -> (12, -9) Net displacement: 12 km east and 9 km south. Distance = sqrt(144 + 81) = sqrt(225) = 15 km Answer: 15 km

Shortcut: Add up the north-south legs and east-west legs separately, then use Pythagoras.

Q17.

Asha starts walking 5 km towards east. Then Asha turns right and walks 5 km. Then Asha turns left and walks 7 km. How far is Asha from the starting point (straight-line distance)?

  1. A17 km
  2. B12 km
  3. C15 km
  4. D13 km
Show answer & solution

Answer: D. 13 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 5 km east -> (5, 0) Leg 2: turn right, walk 5 km south -> (5, -5) Leg 3: turn left, walk 7 km east -> (12, -5) Net displacement: 12 km east and 5 km south. Distance = sqrt(144 + 25) = sqrt(169) = 13 km Answer: 13 km

Shortcut: Add up the north-south legs and east-west legs separately, then use Pythagoras.

Q18.

Meena starts walking 6 km towards south. Then Meena turns right and walks 6 km. Then Meena turns left and walks 2 km. How far is Meena from the starting point (straight-line distance)?

  1. A14 km
  2. B8 km
  3. C10 km
  4. D12 km
Show answer & solution

Answer: C. 10 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 6 km south -> (0, -6) Leg 2: turn right, walk 6 km west -> (-6, -6) Leg 3: turn left, walk 2 km south -> (-6, -8) Net displacement: 6 km west and 8 km south. Distance = sqrt(36 + 64) = sqrt(100) = 10 km Answer: 10 km

Shortcut: Add up the north-south legs and east-west legs separately, then use Pythagoras.

Q19.

Kiran starts walking 12 km towards east. Then Kiran turns left and walks 6 km. Then Kiran turns left and walks 9 km. Then Kiran turns left and walks 2 km. How far is Kiran from the starting point (straight-line distance)?

  1. A29 km
  2. B5 km
  3. C7 km
  4. D4 km
Show answer & solution

Answer: B. 5 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 12 km east -> (12, 0) Leg 2: turn left, walk 6 km north -> (12, 6) Leg 3: turn left, walk 9 km west -> (3, 6) Leg 4: turn left, walk 2 km south -> (3, 4) Net displacement: 3 km east and 4 km north. Distance = sqrt(9 + 16) = sqrt(25) = 5 km Answer: 5 km

Shortcut: Add up the north-south legs and east-west legs separately, then use Pythagoras.

Q20.

Suresh starts walking 5 km towards south. Then Suresh turns left and walks 9 km. Then Suresh turns right and walks 3 km. Then Suresh turns right and walks 3 km. How far is Suresh from the starting point (straight-line distance)?

  1. A20 km
  2. B10 km
  3. C14 km
  4. D8 km
Show answer & solution

Answer: B. 10 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 5 km south -> (0, -5) Leg 2: turn left, walk 9 km east -> (9, -5) Leg 3: turn right, walk 3 km south -> (9, -8) Leg 4: turn right, walk 3 km west -> (6, -8) Net displacement: 6 km east and 8 km south. Distance = sqrt(36 + 64) = sqrt(100) = 10 km Answer: 10 km

Shortcut: Add up the north-south legs and east-west legs separately, then use Pythagoras.

Q21.

Neha starts walking 8 km towards west. Then Neha turns left and walks 4 km. Then Neha turns left and walks 12 km. Then Neha turns left and walks 7 km. How far is Neha from the starting point (straight-line distance)?

  1. A5 km
  2. B31 km
  3. C7 km
  4. D4 km
Show answer & solution

Answer: A. 5 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 8 km west -> (-8, 0) Leg 2: turn left, walk 4 km south -> (-8, -4) Leg 3: turn left, walk 12 km east -> (4, -4) Leg 4: turn left, walk 7 km north -> (4, 3) Net displacement: 4 km east and 3 km north. Distance = sqrt(16 + 9) = sqrt(25) = 5 km Answer: 5 km

Shortcut: Add up the north-south legs and east-west legs separately, then use Pythagoras.

Q22.

Anita starts walking 2 km towards west. Then Anita turns left and walks 5 km. Then Anita turns left and walks 2 km. In which direction is the starting point with respect to Anita's final position?

  1. ASouth
  2. BEast
  3. CNorth
  4. DWest
Show answer & solution

Answer: C. North

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 2 km west -> (-2, 0) Leg 2: turn left, walk 5 km south -> (-2, -5) Leg 3: turn left, walk 2 km east -> (0, -5) The end point lies South of the start, so the start lies in the opposite direction, North, from the end point. Answer: North

Shortcut: Net east-west and net north-south displacement decide the direction; equal amounts give a diagonal.

Q23.

Karan starts walking 7 km towards east. Then Karan turns left and walks 6 km. Then Karan turns left and walks 7 km. In which direction is the starting point with respect to Karan's final position?

  1. ANorth
  2. BSouth
  3. CWest
  4. DEast
Show answer & solution

Answer: B. South

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 7 km east -> (7, 0) Leg 2: turn left, walk 6 km north -> (7, 6) Leg 3: turn left, walk 7 km west -> (0, 6) The end point lies North of the start, so the start lies in the opposite direction, South, from the end point. Answer: South

Shortcut: Net east-west and net north-south displacement decide the direction; equal amounts give a diagonal.

Q24.

Lata starts walking 2 km towards south. Then Lata turns left and walks 2 km. Then Lata turns left and walks 2 km. Then Lata turns left and walks 4 km. In which direction is the starting point with respect to Lata's final position?

  1. AEast
  2. BWest
  3. CSouth
  4. DNorth
Show answer & solution

Answer: A. East

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 2 km south -> (0, -2) Leg 2: turn left, walk 2 km east -> (2, -2) Leg 3: turn left, walk 2 km north -> (2, 0) Leg 4: turn left, walk 4 km west -> (-2, 0) The end point lies West of the start, so the start lies in the opposite direction, East, from the end point. Answer: East

Shortcut: Net east-west and net north-south displacement decide the direction; equal amounts give a diagonal.

Q25.

Ravi starts walking 2 km towards east. Then Ravi turns right and walks 3 km. Then Ravi turns left and walks 4 km. Then Ravi turns right and walks 3 km. In which direction is the starting point with respect to Ravi's final position?

  1. ANorth-West
  2. BSouth-East
  3. CNorth-East
  4. DSouth-West
Show answer & solution

Answer: A. North-West

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 2 km east -> (2, 0) Leg 2: turn right, walk 3 km south -> (2, -3) Leg 3: turn left, walk 4 km east -> (6, -3) Leg 4: turn right, walk 3 km south -> (6, -6) The end point lies South-East of the start, so the start lies in the opposite direction, North-West, from the end point. Answer: North-West

Shortcut: Net east-west and net north-south displacement decide the direction; equal amounts give a diagonal.

Q26.

Asha starts walking 4 km towards south. Then Asha turns left and walks 8 km. Then Asha turns left and walks 8 km. Then Asha turns left and walks 8 km. In which direction is the starting point with respect to Asha's final position?

  1. ANorth
  2. BWest
  3. CEast
  4. DSouth
Show answer & solution

Answer: D. South

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 4 km south -> (0, -4) Leg 2: turn left, walk 8 km east -> (8, -4) Leg 3: turn left, walk 8 km north -> (8, 4) Leg 4: turn left, walk 8 km west -> (0, 4) The end point lies North of the start, so the start lies in the opposite direction, South, from the end point. Answer: South

Shortcut: Net east-west and net north-south displacement decide the direction; equal amounts give a diagonal.

Q27.

Divya is facing east. Divya turns 45° to the left, then 90° to the left, then 135° to the left. In which direction is Divya facing now?

  1. ANorth
  2. BWest
  3. CSouth
  4. DEast
Show answer & solution

Answer: C. South

Solution

Start: facing East. Turning right adds the angle clockwise and turning left subtracts it. turn 45 degrees left -> facing North-East turn 90 degrees left -> facing North-West turn 135 degrees left -> facing South Answer: South

Shortcut: Clockwise order: N, NE, E, SE, S, SW, W, NW. Right turn moves forward in this list, left turn moves back.

Q28.

Imran is facing south. Imran turns 90° to the right, then 135° to the left, then 45° to the right. In which direction is Imran facing now?

  1. ANorth
  2. BWest
  3. CSouth
  4. DEast
Show answer & solution

Answer: C. South

Solution

Start: facing South. Turning right adds the angle clockwise and turning left subtracts it. turn 90 degrees right -> facing West turn 135 degrees left -> facing South-East turn 45 degrees right -> facing South Answer: South

Shortcut: Clockwise order: N, NE, E, SE, S, SW, W, NW. Right turn moves forward in this list, left turn moves back.

Q29.

One evening just before sunset, Vikram was standing facing a pole. The shadow of the pole fell exactly to the right of Vikram. Which direction was Vikram facing?

  1. AEast
  2. BSouth
  3. CWest
  4. DNorth
Show answer & solution

Answer: D. North

Solution

The sun is in the west just before sunset, so the shadow falls towards the east. The shadow is right of Vikram's facing direction, so east is right of the facing direction. The direction to the right of North is east. Answer: North

Shortcut: Morning shadow points west, evening shadow points east (sun is opposite to the shadow).

Q30.

One morning just after sunrise, Anita was standing facing a pole. The shadow of the pole fell exactly behind Anita. Which direction was Anita facing?

  1. ANorth
  2. BSouth
  3. CEast
  4. DWest
Show answer & solution

Answer: C. East

Solution

The sun is in the east just after sunrise, so the shadow falls towards the west. The shadow is behind of Anita's facing direction, so west is behind of the facing direction. West is behind, so Anita faces the opposite direction, East. Answer: East

Shortcut: Morning shadow points west, evening shadow points east (sun is opposite to the shadow).

Q31.

The post office is 2 m to the east of the library. The bank is 6 m to the east of the post office. The market is 6 m to the east of the bank. In which direction is the market with respect to the library?

  1. AWest
  2. BSouth
  3. CEast
  4. DNorth
Show answer & solution

Answer: C. East

Solution

Take the library as (0,0). the post office is 2 m east of the library -> (2, 0) the bank is 6 m east of the post office -> (8, 0) the market is 6 m east of the bank -> (14, 0) So the market lies due east of the library. Answer: East

Shortcut: Mark each position on a quick grid; equal east-west and north-south offsets give a diagonal direction.

Q32.

N is 8 m to the north of M. O is 3 m to the south of N. T is 5 m to the west of O. In which direction is T with respect to M?

  1. ASouth-East
  2. BNorth-West
  3. CNorth-East
  4. DSouth-West
Show answer & solution

Answer: B. North-West

Solution

Take M as (0,0). N is 8 m north of M -> (0, 8) O is 3 m south of N -> (0, 5) T is 5 m west of O -> (-5, 5) So T is 5 m west and 5 m north of M, i.e. towards North-West. Answer: North-West

Shortcut: Mark each position on a quick grid; equal east-west and north-south offsets give a diagonal direction.

Q33.

A tree is 3 m to the south of a well. A pole is 6 m to the north of a tree. A shop is 7 m to the north of a pole. In which direction is a shop with respect to a well?

  1. ASouth
  2. BNorth
  3. CEast
  4. DWest
Show answer & solution

Answer: B. North

Solution

Take a well as (0,0). a tree is 3 m south of a well -> (0, -3) a pole is 6 m north of a tree -> (0, 3) a shop is 7 m north of a pole -> (0, 10) So a shop lies due north of a well. Answer: North

Shortcut: Mark each position on a quick grid; equal east-west and north-south offsets give a diagonal direction.

Q34.

Arjun starts walking 6 km towards south. Then Arjun turns right and walks 6 km. Then Arjun turns left and walks 2 km. Arjun then walks back to the starting point in a straight line. What is the total distance Arjun has walked?

  1. A14 km
  2. B24 km
  3. C28 km
  4. D10 km
Show answer & solution

Answer: B. 24 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 6 km south -> (0, -6) Leg 2: turn right, walk 6 km west -> (-6, -6) Leg 3: turn left, walk 2 km south -> (-6, -8) Distance walked before returning = 6 + 6 + 2 = 14 km Straight-line return = sqrt(36 + 64) = 10 km Total = 14 + 10 = 24 km Answer: 24 km

Shortcut: Total path = sum of legs + straight-line distance back to the start.

Q35.

Divya starts walking 3 km towards north. Then Divya turns left and walks 6 km. Then Divya turns left and walks 11 km. Divya then walks back to the starting point in a straight line. What is the total distance Divya has walked?

  1. A30 km
  2. B20 km
  3. C40 km
  4. D34 km
Show answer & solution

Answer: A. 30 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 3 km north -> (0, 3) Leg 2: turn left, walk 6 km west -> (-6, 3) Leg 3: turn left, walk 11 km south -> (-6, -8) Distance walked before returning = 3 + 6 + 11 = 20 km Straight-line return = sqrt(36 + 64) = 10 km Total = 20 + 10 = 30 km Answer: 30 km

Shortcut: Total path = sum of legs + straight-line distance back to the start.

Hard questions

Q36.

Arjun starts walking 4 km towards west. Then Arjun turns right and walks 10 km. Then Arjun turns right and walks 5 km. Then Arjun turns right and walks 7 km. Then Arjun turns right and walks 5 km. How far is Arjun from the starting point (straight-line distance)?

  1. A31 km
  2. B7 km
  3. C4 km
  4. D5 km
Show answer & solution

Answer: D. 5 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 4 km west -> (-4, 0) Leg 2: turn right, walk 10 km north -> (-4, 10) Leg 3: turn right, walk 5 km east -> (1, 10) Leg 4: turn right, walk 7 km south -> (1, 3) Leg 5: turn right, walk 5 km west -> (-4, 3) Net displacement: 4 km west and 3 km north. Distance = sqrt(16 + 9) = sqrt(25) = 5 km Answer: 5 km

Shortcut: Add up the north-south legs and east-west legs separately, then use Pythagoras.

Q37.

Divya starts walking 4 km towards south. Then Divya turns right and walks 6 km. Then Divya turns left and walks 12 km. Then Divya turns right and walks 14 km. Then Divya turns left and walks 5 km. How far is Divya from the starting point (straight-line distance)?

  1. A41 km
  2. B21 km
  3. C29 km
  4. D31 km
Show answer & solution

Answer: C. 29 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 4 km south -> (0, -4) Leg 2: turn right, walk 6 km west -> (-6, -4) Leg 3: turn left, walk 12 km south -> (-6, -16) Leg 4: turn right, walk 14 km west -> (-20, -16) Leg 5: turn left, walk 5 km south -> (-20, -21) Net displacement: 20 km west and 21 km south. Distance = sqrt(400 + 441) = sqrt(841) = 29 km Answer: 29 km

Shortcut: Add up the north-south legs and east-west legs separately, then use Pythagoras.

Q38.

Imran starts walking 10 km towards east. Then Imran turns left and walks 8 km. Then Imran turns right and walks 6 km. Then Imran turns left and walks 11 km. Then Imran turns right and walks 14 km. Then Imran turns right and walks 3 km. How far is Imran from the starting point (straight-line distance)?

  1. A52 km
  2. B46 km
  3. C34 km
  4. D30 km
Show answer & solution

Answer: C. 34 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 10 km east -> (10, 0) Leg 2: turn left, walk 8 km north -> (10, 8) Leg 3: turn right, walk 6 km east -> (16, 8) Leg 4: turn left, walk 11 km north -> (16, 19) Leg 5: turn right, walk 14 km east -> (30, 19) Leg 6: turn right, walk 3 km south -> (30, 16) Net displacement: 30 km east and 16 km north. Distance = sqrt(900 + 256) = sqrt(1156) = 34 km Answer: 34 km

Shortcut: Add up the north-south legs and east-west legs separately, then use Pythagoras.

Q39.

Priya starts walking 7 km towards north. Then Priya turns left and walks 7 km. Then Priya turns left and walks 9 km. Then Priya turns left and walks 13 km. Then Priya turns right and walks 14 km. Then Priya turns left and walks 6 km. How far is Priya from the starting point (straight-line distance)?

  1. A56 km
  2. B20 km
  3. C28 km
  4. D16 km
Show answer & solution

Answer: B. 20 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 7 km north -> (0, 7) Leg 2: turn left, walk 7 km west -> (-7, 7) Leg 3: turn left, walk 9 km south -> (-7, -2) Leg 4: turn left, walk 13 km east -> (6, -2) Leg 5: turn right, walk 14 km south -> (6, -16) Leg 6: turn left, walk 6 km east -> (12, -16) Net displacement: 12 km east and 16 km south. Distance = sqrt(144 + 256) = sqrt(400) = 20 km Answer: 20 km

Shortcut: Add up the north-south legs and east-west legs separately, then use Pythagoras.

Q40.

Karan and Lata start from the same point. Karan walks 8 km north and then turns east and walks 3 km. Lata walks 10 km east and then turns south and walks 16 km. How far apart are they now?

  1. A25 km
  2. B31 km
  3. C37 km
  4. D15 km
Show answer & solution

Answer: A. 25 km

Solution

Take the start as (0,0). Karan: 8 km north -> (0,8); 3 km east -> (3,8) Lata: 10 km east -> (10,0); 16 km south -> (10,-16) Horizontal gap = |3 - 10| = 7 km; vertical gap = 8 + 16 = 24 km Distance = sqrt(49 + 576) = sqrt(625) = 25 km Answer: 25 km

Shortcut: Find both end points as coordinates, then take the difference in each direction and use Pythagoras.

Q41.

Ravi and Asha start from the same point. Ravi walks 18 km north and then turns east and walks 6 km. Asha walks 13 km east and then turns south and walks 6 km. How far apart are they now?

  1. A31 km
  2. B43 km
  3. C19 km
  4. D25 km
Show answer & solution

Answer: D. 25 km

Solution

Take the start as (0,0). Ravi: 18 km north -> (0,18); 6 km east -> (6,18) Asha: 13 km east -> (13,0); 6 km south -> (13,-6) Horizontal gap = |6 - 13| = 7 km; vertical gap = 18 + 6 = 24 km Distance = sqrt(49 + 576) = sqrt(625) = 25 km Answer: 25 km

Shortcut: Find both end points as coordinates, then take the difference in each direction and use Pythagoras.

Q42.

Meena and Kiran start from the same point. Meena walks 12 km north and then turns east and walks 19 km. Kiran walks 12 km east and then turns south and walks 12 km. How far apart are they now?

  1. A31 km
  2. B55 km
  3. C25 km
  4. D7 km
Show answer & solution

Answer: C. 25 km

Solution

Take the start as (0,0). Meena: 12 km north -> (0,12); 19 km east -> (19,12) Kiran: 12 km east -> (12,0); 12 km south -> (12,-12) Horizontal gap = |19 - 12| = 7 km; vertical gap = 12 + 12 = 24 km Distance = sqrt(49 + 576) = sqrt(625) = 25 km Answer: 25 km

Shortcut: Find both end points as coordinates, then take the difference in each direction and use Pythagoras.

Q43.

Suresh and Neha start from the same point. Suresh walks 10 km north and then turns east and walks 20 km. Neha walks 4 km east and then turns south and walks 20 km. How far apart are they now?

  1. A46 km
  2. B54 km
  3. C34 km
  4. D26 km
Show answer & solution

Answer: C. 34 km

Solution

Take the start as (0,0). Suresh: 10 km north -> (0,10); 20 km east -> (20,10) Neha: 4 km east -> (4,0); 20 km south -> (4,-20) Horizontal gap = |20 - 4| = 16 km; vertical gap = 10 + 20 = 30 km Distance = sqrt(256 + 900) = sqrt(1156) = 34 km Answer: 34 km

Shortcut: Find both end points as coordinates, then take the difference in each direction and use Pythagoras.

Q44.

Imran starts walking 3 km towards west. Then Imran turns left and walks 2 km. Then Imran turns right and walks 12 km. Then Imran turns right and walks 10 km. Imran then walks back to the starting point in a straight line. What is the total distance Imran has walked?

  1. A27 km
  2. B54 km
  3. C50 km
  4. D44 km
Show answer & solution

Answer: D. 44 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 3 km west -> (-3, 0) Leg 2: turn left, walk 2 km south -> (-3, -2) Leg 3: turn right, walk 12 km west -> (-15, -2) Leg 4: turn right, walk 10 km north -> (-15, 8) Distance walked before returning = 3 + 2 + 12 + 10 = 27 km Straight-line return = sqrt(225 + 64) = 17 km Total = 27 + 17 = 44 km Answer: 44 km

Shortcut: Total path = sum of legs + straight-line distance back to the start.

Q45.

Priya starts walking 10 km towards north. Then Priya turns left and walks 12 km. Then Priya turns left and walks 10 km. Then Priya turns left and walks 3 km. Then Priya turns left and walks 12 km. Priya then walks back to the starting point in a straight line. What is the total distance Priya has walked?

  1. A47 km
  2. B94 km
  3. C68 km
  4. D62 km
Show answer & solution

Answer: D. 62 km

Solution

Start at (0,0) (east = +x, north = +y). Leg 1: walk 10 km north -> (0, 10) Leg 2: turn left, walk 12 km west -> (-12, 10) Leg 3: turn left, walk 10 km south -> (-12, 0) Leg 4: turn left, walk 3 km east -> (-9, 0) Leg 5: turn left, walk 12 km north -> (-9, 12) Distance walked before returning = 10 + 12 + 10 + 3 + 12 = 47 km Straight-line return = sqrt(81 + 144) = 15 km Total = 47 + 15 = 62 km Answer: 62 km

Shortcut: Total path = sum of legs + straight-line distance back to the start.

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