A, B, C, D and E are standing in a line facing north. E is standing 40 metres to the left of B. A is standing 20 metres to the left of C. D is standing 20 metres to the right of E and 50 metres to the right of C. With respect to D, where is B standing?

Introduction / Context:
This problem deals with a linear arrangement on a number line measured in metres, with everyone facing north. Instead of discrete seats, the positions are given as distances to the left or right of each other. The task is to translate the verbal geometric descriptions into coordinates on a line and then determine the relative position of one person with respect to another. Questions like this test algebraic thinking and spatial interpretation together.

Given Data / Assumptions:

• The five people A, B, C, D and E stand on a straight line facing north.
• E is 40 metres to the left of B.
• A is 20 metres to the left of C.
• D is 20 metres to the right of E.
• D is also 50 metres to the right of C.
• Left and right are measured from the perspective of a person facing north, so left corresponds to west and right to east on a horizontal number line.

Concept / Approach:
We model the line as a one dimensional axis. Let us assume a coordinate for B and then derive coordinates for E, D, C and A using the given distances. Once we establish a consistent set of positions, the relative location of B with respect to D is simply the difference of their coordinates. This approach helps avoid confusion that sometimes arises from manipulating left and right statements directly in words.

Step-by-Step Solution:
Step 1: Assume B stands at coordinate 0 for convenience.Step 2: E is 40 metres to the left of B, so E stands at coordinate -40.Step 3: D is 20 metres to the right of E, so D stands at -40 + 20 = -20.Step 4: D is also 50 metres to the right of C. Therefore, C must stand at coordinate -20 - 50 = -70.Step 5: A is 20 metres to the left of C, so A stands at -70 - 20 = -90.Step 6: We now have consistent positions: A at -90, C at -70, E at -40, D at -20, and B at 0.Step 7: The question asks for the position of B with respect to D. Since D is at -20 and B at 0, B is 20 metres to the right (east) of D.

Verification / Alternative check:
We can cross check the relations. E is indeed 40 metres left of B because -40 is 40 units less than 0. D is 20 metres right of E since -20 is 20 units greater than -40. D is 50 metres right of C because -20 is 50 units greater than -70. A is 20 metres left of C since -90 is 20 units less than -70. All conditions are satisfied, so the coordinate assignment is correct and the derived relation between B and D is reliable.

Why Other Options Are Wrong:
Option B (30 metres right) and Option C (40 metres right) overstate the distance between B and D. Option D (40 metres left) reverses the direction and also changes the magnitude. A gap of exactly 20 metres separates D and B in the eastward direction, so only option A correctly states that B stands 20 metres to the right of D.

Common Pitfalls:
Students often get confused switching between left right descriptions from different reference persons. A robust way is to fix one coordinate system and stick to it, treating all positions relative to a chosen origin. Another pitfall is misreading phrases like right of C or left of B as right of D, which leads to inconsistent distances. Working carefully through each relationship and drawing a number line can help avoid these errors.

Final Answer:
B is standing 20 metres to the right of D, therefore the correct option is “20 metres right”.