Direction and distance for RRB NTPC: turns, shortest distance and shadows

Direction questions describe a walk: so many kilometres north, a turn, so many more, another turn. Then they ask where the person ends up, how far from the start, or which way they now face. With a sketch, most of these take under a minute. Without one, even a three-turn question can go wrong, because "turn left" means a different direction depending on which way you are facing.

In NTPC this topic shows up as plain walks, "which way is X from Y" questions, degree rotations and sun-and-shadow questions. One method covers them all.

The eight directions

Draw north at the top, south at the bottom, east on the right and west on the left. Between them are north-east (NE), south-east (SE), south-west (SW) and north-west (NW).

Measured clockwise from north: N 0°, NE 45°, E 90°, SE 135°, S 180°, SW 225°, W 270°, NW 315°. This helps with rotation questions.

Turning left and right

• A right turn is 90° clockwise. A left turn is 90° anticlockwise.
• The turn depends on the direction you are facing now, not on north.
• A quick check: facing south, your right hand points west.

A method

1. Mark the start with a dot and write "S" beside it.
2. Draw each leg as an arrow with its length, and write the direction you are now facing at the tip.
3. Turn from the arrow's direction, using the table above, before drawing the next leg.
4. Find the net movement: total east minus total west, and total north minus total south.
5. Shortest distance = √(x² + y²), where x and y are the net east–west and north–south movements.
6. Direction from the start comes from the signs: net north and net east means north-east, and so on.

Look out for the Pythagorean triplets 3-4-5, 6-8-10, 5-12-13 and 8-15-17. NTPC distances are usually built on them.

Sun and shadow

• The sun rises in the east, so in the morning shadows fall to the west.
• The sun sets in the west, so in the evening shadows fall to the east.
• At noon, shadows are shortest. For most of India through most of the year the noon sun is to the south, so the shadow falls roughly north. Exam questions rarely use noon.

To solve a shadow question: fix where the shadow points, then work out which way the person faces so that the shadow is on the side the question says.

Worked questions

Q1. A person walks 5 km north, turns right and walks 3 km, then turns right again and walks 5 km. Where are they from the start?

Facing north, right is east: 3 km east. Facing east, right is south: 5 km south. North 5 and south 5 cancel. The person is 3 km east of the start.

Q2. A person walks 6 km east and then 8 km north. What is the shortest distance from the start, and in which direction?

√(6² + 8²) = √(36 + 64) = √100 = 10 km, towards the north-east.

Q3. A person walks 5 km south, turns left and walks 8 km, turns left and walks 11 km, then turns left and walks 8 km. Where are they now?

• South 5. Facing south, left is east: 8 km east.
• Facing east, left is north: 11 km north.
• Facing north, left is west: 8 km west.
• East 8 and west 8 cancel. North 11 minus south 5 leaves 6 north. The person is 6 km north of the start.

Q4. A person walks 9 km north, turns right and walks 4 km, turns right and walks 3 km, then turns left and walks 4 km. How far are they from the start?

• North 9. Right from north is east: 4 km east.
• Right from east is south: 3 km south.
• Left from south is east: 4 km east.
• Net: north 9 − 3 = 6; east 4 + 4 = 8. Distance √(36 + 64) = 10 km, to the north-east.

Q5. A person faces north, turns 90° clockwise, then turns 180°. Which way do they face now?

North → east (90° clockwise) → west (180° from east).

Q6. A person faces north-east and turns 135° clockwise. Which way do they face?

North-east is 45°. 45° + 135° = 180°, which is south.

Q7. In the morning, a person's shadow falls to their right. Which direction are they facing?

Morning shadows fall to the west, so the person's right is west. Someone whose right hand points west is facing south.

Common mistakes

• Turning as if always facing north. After a left turn from south, you face east, not west.
• Adding all distances instead of finding net movement in each direction.
• Answering the reverse direction (person from start vs start from person).
• Mixing up morning and evening shadows. Morning: shadow west. Evening: shadow east.
• Skipping the sketch because the question looks short.

Practice set

1. A person walks 10 m south, turns left and walks 10 m. In which direction are they from the start?
2. A person walks 3 km west and then 4 km north. What is the shortest distance from the start?
3. Facing east, a person turns 90° anticlockwise. Which way do they face?
4. A person walks 4 km north, turns left and walks 6 km, then turns left and walks 4 km. How far are they from the start, and in which direction?
5. In the evening, a person's shadow falls to their left. Which direction are they facing?
6. A person faces south-west, turns 90° clockwise, and then turns 180° anticlockwise. Which way do they face now?
7. A person walks 12 km east, turns left and walks 5 km. What is the shortest distance from the start, and in which direction?
8. X is 4 km north of Y. Z is 3 km east of Y. How far is X from Z, and in which direction?

Answers:

1. South-east. Facing south, left is east.
2. 5 km. √(9 + 16) = 5, towards the north-west.
3. North.
4. 6 km west. North 4, west 6, south 4; north and south cancel.
5. South. Evening shadows fall east; facing south, east is on the left.
6. South-east. SW is 225°; + 90° gives 315° (NW); − 180° gives 135° (SE).
7. 13 km, north-east. Facing east, left is north; √(144 + 25) = √169 = 13.
8. 5 km, north-west. From Z, X is 3 km west and 4 km north; √(9 + 16) = 5.

What to do next

• For your next 20 questions, write the facing direction at the tip of every arrow.
• Learn the four triplets (3-4-5, 6-8-10, 5-12-13, 8-15-17).
• Practise ten "start from person" questions to lock in the reverse-direction habit.
• Next, work through order and ranking, and revisit blood relations for more diagram practice.