Direction sense for RRB Group D

A direction question walks a person around: north for 5 km, turn right, walk 3 km, turn right again. Then it asks where they are, how far they are from the start, or which way they face. Every step is easy. The mistakes come from turning the wrong way, or from holding the whole walk in your head.

So the rule for this topic is: draw every question. A rough sketch with arrows takes 15 seconds and is almost never wrong. This guide gives you the turn rules, the distance method, the shadow rule and a practice set.

The eight directions

Draw a plus sign. North is at the top, south at the bottom, east on the right and west on the left. The four in-between directions sit on the diagonals.

Neighbouring directions on this eight-point compass are 45° apart. North to east is 90°. North to south is 180°.

Turning left and right

A right turn is 90° clockwise. A left turn is 90° anticlockwise. What matters is the way the person is facing before the turn, not north on your page.

Some questions give turns in degrees. Count in steps of 45°: from north, 45° clockwise is north-east, 90° is east, 135° is south-east, and so on. Two right turns make an about-turn, so the person faces the opposite way.

Distance from the start

To find how far someone ends up from the start:

1. Add up all the east–west movement, counting east as + and west as −. Call the total x.
2. Add up all the north–south movement, counting north as + and south as −. Call it y.
3. If one of them is zero, the distance is simply the other one.
4. Otherwise, the distance is √(x² + y²), by Pythagoras.

The direction from the start comes from the signs. Positive x and positive y means north-east. Positive x and negative y means south-east, and so on.

Shadows

The sun rises in the east and sets in the west, and a shadow always points away from the sun.

So in the morning, a person facing north has their shadow on their left. A person facing south has it on their right.

Worked examples

Example 1: A person walks 8 km east, turns left and walks 6 km. How far are they from the start, and in which direction?

• Left of east is north. So the walk is east 8, then north 6.
• Distance = √(8² + 6²) = √(64 + 36) = √100 = 10 km. Direction: north-east.

Example 2: Someone faces south, turns right, then turns right again. Which way do they face now?

• South, then right = west, then right = north. Two right turns reverse the direction.

Example 3: A person walks 5 km north, turns right and walks 3 km, then turns right again and walks 5 km. Where are they now?

• North 5, then east 3, then south 5. North and south cancel.
• They are 3 km east of the start.

Example 4: A person walks 3 km north, turns right and walks 5 km, turns right and walks 8 km, then turns left and walks 7 km. How far are they from the start, and in which direction?

• North 3, then east 5 (right of north), then south 8 (right of east), then east 7 (left of south).
• East–west: 5 + 7 = 12 east. North–south: 3 − 8 = 5 south.
• Distance = √(12² + 5²) = √169 = 13 km, towards the south-east.

Example 5: A person faces north, turns 90° clockwise, then 135° anticlockwise. Which way are they facing?

• 90° clockwise from north is east.
• From east, 135° anticlockwise: 90° brings them to north, and 45° more brings them to north-west.

Example 6: In the evening, a person's shadow falls straight in front of them. Which way are they facing?

• Evening shadows fall to the east. The shadow is in front, so the person faces east.

Common mistakes

• Turning as if the person always faced north.
• Adding every distance instead of finding the net movement. Walking 5 north and 5 south brings you back to where you started.
• Mixing up the morning and evening shadow rules.
• Giving the direction of the start from the person instead of the person from the start. Read the last line carefully: "in which direction is the person from the start?"

Practice set

1. A person walks 12 m west and then 5 m north. How far are they from the start?
2. Facing east, a person turns left twice. Which way do they face?
3. A person walks 10 km south, turns left and walks 10 km. In which direction are they from the start?
4. In the morning, a person's shadow falls to their left. Which way are they facing?
5. A person walks 6 km north, turns right and walks 4 km, then turns right and walks 6 km. Where are they now?
6. Facing west, a person turns 45° clockwise. Which way do they face?
7. A person walks 6 km east, turns right and walks 3 km, then turns right and walks 10 km. How far are they from the start, and in which direction?
8. At 7 a.m., a person's shadow falls to their right. Which way are they facing?

Answers:

1. 13 m. √(12² + 5²) = √169 = 13.
2. West. East, then left = north, then left = west.
3. South-east. Left of south is east, so the walk is south 10, then east 10.
4. North. Morning shadows fall west, and west is on your left when you face north.
5. 4 km east of the start. North 6, east 4, south 6. North and south cancel.
6. North-west. 45° clockwise from west is north-west.
7. 5 km, south-west. East 6, south 3, west 10. Net: 4 km west and 3 km south, so √(16 + 9) = 5.
8. South. At 7 a.m. the shadow falls west, and west is on your right when you face south.

What to do next

• Draw the compass with eight directions and the turn table once from memory.
• Solve 10 direction questions a day for a week, sketching every one.
• Learn the four Pythagoras triplets above.
• Next, practise ranking and order, and revise blood relations, which also rewards drawing.