Turns and the compass

The four main directions are north, east, south and west in clockwise order, with north-east, south-east, south-west and north-west midway between them. Every turn is read from the direction the person is currently facing, never from the page. A right turn is 90 degrees clockwise and a left turn is 90 degrees anticlockwise.

The frequent slip is the reversed frame: a person walking south who turns left is now heading east, because east lies on the left of someone facing south. For multi-step turns stated in degrees, add clockwise movement and subtract anticlockwise movement, then convert the net angle back to a direction.

Net displacement

Reduce any path to its net north-south movement and net east-west movement. If both are non-zero, the shortest distance is the hypotenuse: the square root of the sum of their squares. The direction combines both components, such as north-east or south-west.

Worked case: walk 6 km north, then turn right and walk 8 km. The net movement is 6 km north and 8 km east. Distance from the start = √(6² + 8²) = √100 = 10 km, in the north-east quadrant. Strictly, the bearing is about 53° east of north, not exactly 45°, but options use the eight compass labels, so the answer is “north-east”. Remove movements that cancel (5 km south and later 5 km north) before calculating.

Shadow questions

Exam convention: the sun rises exactly in the east and sets exactly in the west, and there is no usable shadow at noon. Questions therefore avoid noon. (In reality, sunrise and sunset shift north or south of due east and west with the seasons. Over most of India, a noon shadow is short and usually points roughly north.) Once the shadow direction is fixed, the problem becomes a facing problem:

• Morning, shadow directly behind: the shadow points west, so the person faces east.
• Morning, shadow on the right: the person faces south.
• Evening, shadow directly in front: the shadow points east, so the person faces east as well.
• Evening, shadow on the left: the person faces south.

Read the side carefully.

Rotated and coded directions

When a question renames directions (for example, north is called south-east), the whole compass has been rotated by a fixed angle. Take degrees clockwise from north: N 0°, NE 45°, E 90°, SE 135°, S 180°, SW 225°, W 270°, NW 315°. North → south-east is +135°. Apply the same rotation to the direction asked: west 270° + 135° = 405° − 360° = 45° = north-east. Check the rotation on a second pair the question gives, because some questions use a reflection rather than a rotation.

Ranking formulas

• Total in a row = position from left + position from right − 1.
• Position from the other end = total − known position + 1.
• The same rules apply to top and bottom ranks in a class, provided no two students share a rank.

A student 17th from the top in a class of 45 is 45 − 17 + 1 = 29th from the bottom. A person 14th from the left and 23rd from the right stands in a row of 36.

Persons between two positions

When both positions are counted from the same end, the number between them is the difference minus one. P at 8th and Q at 25th from the left have 16 persons between them.

When positions are counted from opposite ends, compare their sum with the total:

• Sum < total (no overlap): between = total − sum. In a row of 50, A 15th from the left and B 20th from the right (31st from the left) have 50 − 35 = 15 persons between them.
• Sum = total: the two stand next to each other, with 0 between.
• Sum = total + 1: both positions refer to the same person.
• Sum > total + 1 (crossed): between = sum − total − 2. In a row of 30, A 20th from the left and B 15th from the right (16th from the left) have 35 − 30 − 2 = 3 persons between them (17th, 18th and 19th).

Convert both to the same end whenever in doubt.

Interchange and minimum-number cases

In an interchange, each person takes the other’s former position. Example: A is 12th from the left and B is 18th from the right. After they interchange, A is 20th from the left. A now stands where B stood, so B’s original place was 20th from the left and 18th from the right. The row has 20 + 18 − 1 = 37 persons, and B is now 12th from the left.

When the total is not given and the order of the two persons is not stated, test both arrangements. Example: A is 10th from the left, B is 15th from the right, and exactly three persons stand between them.

• If A is left of B, B is 14th from the left and the row has 14 + 15 − 1 = 28.
• If B is left of A, B is 6th from the left and the row has 6 + 15 − 1 = 20.

A question asking for the minimum expects 20. Never count the two named persons among those between them.

Key points to remember

Frequently asked questions

How do you find the shortest distance in a direction sense question?

Cancel opposite movements to get the net north–south and east–west distances, then apply Pythagoras: distance = √(NS² + EW²). For example, 6 km north and 8 km east gives 10 km.

Which way does a shadow fall in the morning and evening?

By exam convention the morning sun is in the east, so shadows fall to the west. The evening sun is in the west, so shadows fall to the east. Questions avoid noon.

What is the formula for the total number of persons in a row?

Total = position from left + position from right − 1, because the person is counted from both ends.

How do you find a rank from the other end?

Rank from the other end = total − known rank + 1. For example, 17th from the top in a class of 45 is 29th from the bottom.

How many persons are between two people counted from the same end?

Subtract the smaller position from the larger and then subtract 1. For example, 8th and 25th from the left have 16 persons between them.

Practice: 10 MCQs

Attempt all ten questions, then press Submit. The correct answer and a short explanation appear under every question, followed by your score analysis.

Method notes

• Direction and ranking questions are solved by convention-based reasoning, not statute. Every worked figure and answer on this page was re-solved independently with a drawn compass, degree arithmetic and the position formulas.
• Real-world note: the sun rises due east and sets due west only around the equinoxes. Exam questions assume due east and due west unless stated otherwise.