OBTAINED by ADDING a cumulative percentage of aggregates retained on each of the standard sieves ranging from 80 mm to 150 microns.Fine aggregate is always mixed with proportion to the coarse aggregate and the following formula is used for percentage proportion fine aggregate to coarse aggregate.\(\rm{R=\frac{p_2-p}{p-p_1}\times 100}\)where,R = proportion of fine aggregate to the combined aggregate by weightp1 = fineness modulus of fine aggregatep2 = fineness modulus of coarse aggregatep = desired fineness modulus for concrete mixSolution:The percentage of fine aggregate is given by:\(\frac x1\)= \(\frac{{F{M_{coarse}} - F{M_{combined}}}}{{F{M_{combined}} - F{M_{fine}}}} \times 100 = \;\frac{{7.6 - 6.4}}{{6.4 - 2.8}} \times 100 = 33.33\;\% \)Confusion Point:Concept 1Since in the Qs proportion of fine aggregate in coarse aggregate is asked and total percentage is not given. Then we will use LET,x % = FA and y % = CA and combined (x + y) %.So, x.FA + y.CA = (x + y).Combined,On Solving,As proportion of FA in CA = x / y % = (CA - Combined) / (Combined - FA) % \(\rm{R=\frac{p_2-p}{p-p_1}\times 100}\)Concept 2If given find amount of FA, then the formula will be\(\rm{R=\frac{p_2-p}{p_2-p_1}\times 100}\)