Aggregates MCQ with answer and solution

Concept

Fineness Modulus of Combined Aggregates

Formula

P = [(F_coarse - F_combined) / (F_coarse - F_fine)] × 100

Step-by-step solution

1. Identify given values: F\_coarse = 7.6, F\_fine = 2.8, F\_combined = 6.4. 2. Calculate numerator: 7.6 - 6.4 = 1.2. 3. Calculate denominator: 7.6 - 2.8 = 4.8. 4. Calculate proportion: (1.2 / 4.8) \* 100 = 25%.

Explanation

To find the percentage of fine aggregate (P), use the formula: P = [(F_coarse - F_combined) / (F_coarse - F_fine)] × 100 Substituting the given values: - Fineness modulus of coarse aggregate (F\_coarse) = 7.6 - Fineness modulus of fine aggregate (F\_fine) = 2.8 - Fineness modulus of combined aggregate (F\_combined) = 6.4P = \[(7.6 - 6.4) / (7.6 - 2.8)\] × 100 P = (1.2 / 4.8) × 100 = 25% Therefore, 25% fine aggregate is required in the mixture.

Shortcut

Use the Allegation Rule or remember: Fine % = (Difference between Coarse and Combined) / (Difference between Coarse and Fine) × 100. Quick step:1. Top = 7.6 - 6.4 = 1.2 2. Bottom = 7.6 - 2.8 = 4.8 3. 1.2 / 4.8 = 1/4 = 25%

Common mistake

A common mistake is inverting the formula by putting the difference between combined and fine aggregate in the numerator instead of coarse and combined, which leads to calculating the proportion of coarse aggregate (75% or 66 2/3%) rather than the fine aggregate.