Stair design — compute number of treads from storey height and riser A building’s first storey height is 3.2 m. If each riser is 13 cm, determine the required number of treads for the stair (assume a single run between floor levels, so treads = risers − 1).

Introduction / Context:
Basic stair geometry links total storey rise, riser height, and number of risers/treads. In most building layouts, the number of treads in a straight flight equals the number of risers minus one, because the upper floor or landing serves as the final “step.” This question tests correct interpretation of stair arithmetic and common design convention.

Given Data / Assumptions:

• Total storey rise H = 3.2 m = 320 cm.
• Chosen riser r = 13 cm.
• Single run between ground floor and first-floor landing; top landing is the last step level.
• Hence number of treads = number of risers − 1.

Concept / Approach:
First compute the number of risers as H / r. If this is not an integer, round to the nearest practical integer (commonly up to the next integer to avoid an over-tall riser). Then convert to treads using the conventional relationship. Check that the resulting going (tread depth) meets comfort rules (e.g., 2r + g ≈ 600–650 mm) though this question focuses only on count.

Step-by-Step Solution:

Verification / Alternative check:
If 24 risers were used, each riser = 320 / 24 ≈ 13.33 cm, which exceeds the specified 13 cm. Using 25 risers keeps risers at or below the target value; with a landing at the top, treads remain 24.

Why Other Options Are Wrong:

• 12, 18, 30: Not consistent with the computed riser count.
• 25: Corresponds to risers, not treads; the correct treads are one fewer.

Common Pitfalls:
Equating treads to risers without subtracting one for the top landing; failing to round up the riser count to meet the maximum riser constraint.

Final Answer:
24