Sleeper density rule of thumb: If n is the standard rail length in metres, the typical number of sleepers provided per rail length on Indian Railways usually lies in which range?

Introduction / Context:
Sleeper density (SD) expresses the number of sleepers per rail length, providing a quick guide to support and track stiffness. For a given rail length n (in metres), Indian Railway practice uses simple rules like n + x sleepers, where x depends on traffic, axle loads, and track category.

Given Data / Assumptions:

• n denotes rail length in metres.
• We are considering typical mainline practice for Broad Gauge with conventional ballasted track.
• Answer sought is a customary range used in exams and handbooks.

Concept / Approach:

Higher sleeper density improves load distribution, gauge restraint, and track geometry retention. However, it increases material and maintenance costs. A compromise range widely cited is between n + 3 and n + 6 sleepers per 1 rail length, adapting to traffic and speed demands.

Step-by-Step Solution:

Verification / Alternative check:

Permanent-way manuals provide ranges and specific sleeper densities for different track classes; the exam-standard range commonly quoted is (n + 3) to (n + 6).

Why Other Options Are Wrong:

n to (n + 2) is too sparse; (n + 2) to (n + 4) can be inadequate for heavier traffic; (n + 4) to (n + 5) is a narrower subset of the accepted range and not the typical full range cited.

Common Pitfalls:

Confusing sleeper density with sleeper spacing; forgetting that higher category tracks may adopt the higher end of the range.

Final Answer:

(n + 3) to (n + 6)