Fineness Modulus (FM) blending – compute required proportion (choose the nearest) You are to combine a fine aggregate with FM = 2.6 and a coarse aggregate with FM = 6.8 to obtain a combined FM of 5.4. What percentage of the fine aggregate should be used (choose the nearest among the options)?

Introduction / Context:
Fineness modulus (FM) is a single-number index indicating aggregate coarseness. By blending a fine and a coarse aggregate, a target FM can be achieved for better grading and workability. This is a linear blending problem frequently used in mix design.

Given Data / Assumptions:

• Fine aggregate FM (F1) = 2.6.
• Coarse aggregate FM (F2) = 6.8.
• Target combined FM (Ft) = 5.4.
• Let p = proportion (by mass) of the fine aggregate in the blend.

Concept / Approach:
For two-aggregate blends, combined FM is approximately the weighted average: Ft = pF1 + (1 - p)F2. Solve for p and convert to percentage. Choose the nearest option provided, since plant control and sieve rounding yield small deviations.

Step-by-Step Solution:
Write relation: 5.4 = p2.6 + (1 - p)6.8Expand: 5.4 = 2.6p + 6.8 - 6.8p = 6.8 - 4.2pRearrange: 4.2p = 6.8 - 5.4 = 1.4Compute: p = 1.4 / 4.2 = 0.333… = 33.33%Select the closest among the options: 30%

Verification / Alternative check:
Check with 30% fine: FM = 0.302.6 + 0.706.8 = 0.78 + 4.76 = 5.54 (slightly high). With 40% fine: FM = 5.16 (slightly low). The exact 33.3% lies between; batching tolerances make 30% a reasonable nearest choice for this question.

Why Other Options Are Wrong:

• 40%, 50%, 60%, 20% deviate more from the computed 33.3% than 30% does, based on the provided discrete options.

Common Pitfalls:
Assuming FM blending is non-linear; for practical purposes, linear blending works well when the two aggregates are from stable sources and the same sieve series is used.

Final Answer:
30%