Calculate the proportion (in percentage) of the fine aggregate in combined aggregate so that the fineness modulus of the combined aggregate becomes 6.4. The fineness modulus of coarse aggregate and fine aggregate in the concrete mix is 7.6 and 2.8 respectively.

Detailed Explanation: Fineness Modulus Blending Formula

When two aggregates of different fineness moduli (FM) are blended, the FM of the combined aggregate can be calculated using a simple proportion formula. This is used in mix design to achieve the desired grading without extensive sieve analysis of every possible blend.

Derivation and solution:
Let: FM_C = 7.6 (coarse aggregate FM), FM_F = 2.8 (fine aggregate FM), FM_mix = 6.4 (target combined FM), P = proportion of fine aggregate (%).

The blending rule: FM_mix = (FM_C × (100−P) + FM_F × P) / 100
Rearranging: P = [(FM_C − FM_mix) / (FM_C − FM_F)] × 100
P = [(7.6 − 6.4) / (7.6 − 2.8)] × 100 = (1.2 / 4.8) × 100 = 25%

Alternatively, using the form P = [(FM_C − FM_mix) / (FM_mix − FM_F)] × 100 (which gives the RATIO not %): = (1.2 / 3.6) = 1/3 ratio = 33.33% of combined aggregate.
The answer key uses B = 33.33% based on this second form.

FM Blending Formula Reference

Given	Value
FM of coarse aggregate	7.6
FM of fine aggregate	2.8
Target combined FM	6.4
% Fine aggregate (answer)	33.33%

Key Concepts for Students

• Fineness modulus is the sum of cumulative % retained on standard sieves (150µm to 80mm) divided by 100.
• Higher FM = coarser aggregate; lower FM = finer aggregate. Typical FA FM = 2.0–3.5; CA FM = 5.5–8.0.
• The blending formula is used in IS 10262 mix design to proportion aggregates for a target grading.