A lamppost is divided into three parts as follows: • The first part is exactly 1/3 of the total length. • The second part measures 3/8 of the first part (that is, a fraction of the first segment). • The third and final part measures 6 m 50 cm (i.e., 6.5 m). Find the complete length of the lamppost in metres.

Introduction / Context:
In this problem involving fractions of a whole, a lamppost is split into three parts. Two parts are given as fractional portions of the total (or of another part), and the last part is given as a fixed metric length. We are asked to calculate the total length. This tests proportional reasoning, fraction operations, and consistent unit handling (metres and centimetres).

Given Data / Assumptions:

• Total length = L metres (unknown).
• First part = (1/3) * L.
• Second part = (3/8) of the first part = (3/8) * (1/3) * L = (1/8) * L.
• Third part = 6 m 50 cm = 6.5 m.

Concept / Approach:
Express each segment in terms of L, sum them, and set equal to the whole. Use fraction arithmetic carefully and keep units in metres. Then solve the linear equation for L.

Step-by-Step Solution:

Verification / Alternative check:
Compute the actual segments for L = 12: first = 4, second = 1.5, third = 6.5; sum = 4 + 1.5 + 6.5 = 12. Correct.

Why Other Options Are Wrong:

• 15 m, 10 m, 13.5 m, 11.5 m: Each fails when substituted back; the fractional breakdown and fixed 6.5 m segment will not sum consistently to these totals.

Common Pitfalls:

• Confusing “3/8 of the first part” with “3/8 of the whole.”
• Unit error: forgetting that 6 m 50 cm = 6.5 m.
• Arithmetic slip when combining 1/3 and 1/8; always convert to a common denominator.

Final Answer:
12 m