The percentage of fine aggregate (FM = 2.6) to be combined with coarse aggregate (FM = 6.8) to obtain combined FM = 5.4, is:
Correct Answer: B. 50%
📚 Detailed Explanation: Fineness Modulus Blending Formula
Formula for blending aggregates: When fine aggregate (FM = Y) is mixed with coarse aggregate (FM = X) to obtain a combined FM = Z, the percentage of fine aggregate (P) is:
P = [(X − Z) / (X − Y)] × 100
P = [(X − Z) / (X − Y)] × 100
X = FM of coarse aggregate = 6.8
Y = FM of fine aggregate = 2.6
Z = FM of combined aggregate = 5.4 (as given)
Y = FM of fine aggregate = 2.6
Z = FM of combined aggregate = 5.4 (as given)
P = [(6.8 − 5.4) / (6.8 − 2.6)] × 100
P = [1.4 / 4.2] × 100 = 33.3%
Note: Answer 50% corresponds to FM_combined = 4.7
[0.5 × 2.6 + 0.5 × 6.8 = 4.7, not 5.4]
Verification at P = 50%
| Parameter | Value |
|---|---|
| FM_fine | 2.6 |
| FM_coarse | 6.8 |
| At P = 50%: combined FM | 0.5 × 2.6 + 0.5 × 6.8 = 4.7 (not 5.4) |
| At P = 33.3%: combined FM | 0.333 × 2.6 + 0.667 × 6.8 = 5.4 ✔ |
- Formula: P = [(X − Z) / (X − Y)] × 100 where X = FM coarse, Y = FM fine, Z = FM combined.
- The given answer of 50% corresponds to a combined FM of 4.7, suggesting a possible typographical discrepancy in the question's combined FM value.
- In exam practice: apply the formula with the given numbers; the standard formula is correct.