Two persons P and Q are initially separated by a distance of 20 metres along a west east line, with P in the west and Q in the east. Now P and Q start walking, P towards the north and Q towards the south, and each walks 5 metres. Then both take a right turn and walk 10 metres each. After that, both take a left turn and walk another 5 metres each and stop. What is the distance between P and Q at their final positions?

Introduction / Context:
This direction sense question requires tracking the movements of two people, P and Q, who start at different positions and walk in different directions. After a series of moves and turns, we need to find the distance between their final positions. Questions like this encourage careful use of a coordinate system or diagram to avoid mixing up left and right or miscounting distances.

Given Data / Assumptions:

• Initially, P and Q are 20 metres apart on a west east line, P in the west and Q in the east.
• P walks 5 metres north, Q walks 5 metres south.
• Then both take a right turn and walk 10 metres each.
• After that, both take a left turn and walk 5 metres each.
• Standard convention is used: right turn is clockwise relative to the current facing direction, left is anticlockwise.
• The task is to calculate the straight line distance between P and Q at the end.

Concept / Approach:
We use a simple coordinate system with east as positive x and north as positive y. We set P at (0, 0) and Q at (20, 0) initially. We track each movement of P and Q step by step, updating their coordinates based on direction and distance. The final distance between them is obtained using the distance formula between two points. If this distance does not match any of the explicit numerical options, the correct answer is the option representing none of these.

Step-by-Step Solution:
Step 1: Place P at (0, 0) and Q at (20, 0).Step 2: P walks 5 metres north to (0, 5). Q walks 5 metres south to (20, −5).Step 3: At this stage, P faces north and Q faces south.Step 4: Both take a right turn. P's right from north is east, so P walks 10 metres east to (10, 5). Q's right from south is west, so Q walks 10 metres west to (10, −5).Step 5: Now both face their new directions (P facing east, Q facing west) and then take a left turn. P's left from east is north, so P walks 5 metres north to (10, 10). Q's left from west is south, so Q walks 5 metres south to (10, −10).Step 6: The final coordinates are P at (10, 10) and Q at (10, −10).Step 7: The distance between these points is |10 − (−10)| along the y axis, which equals 20 metres.

Verification / Alternative check:
We can observe that both P and Q end up directly above and below the same x coordinate, x = 10. Their vertical separation is twice the distance from the horizontal axis, since P is 10 units above and Q is 10 units below, making the total vertical separation 20 metres. There is no horizontal separation at the end, so the straight line distance equals this vertical separation. Because 20 metres does not appear among the numeric choices a, b, or c, the answer must be the option that states none of these.

Why Other Options Are Wrong:
The option 15 metres would require each to be 7.5 metres above and below the midline, which does not match the movements. The option 25 metres is larger than any plausible separation given the step sizes. The option 30 metres is even more extreme and has no basis in the described paths. The value 20 metres is correct but appears only indirectly as our calculation, so among the listed options only the choice labelled none of these matches the true situation.

Common Pitfalls:
A common error is to treat right and left turns as absolute directions rather than relative to north and south, which can place P and Q in completely wrong quadrants. Another mistake is to attempt to mentally add distances without using coordinates or a diagram, leading to miscalculations of their final separation. Drawing a coordinate grid or at least a rough sketch and marking each leg of the journey is the safest way to avoid such errors.

Final Answer:
The final distance between P and Q is 20 metres, which does not appear among the explicit numeric options, so the correct choice is None of these.