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The percentage of the fine aggregate of fineness modulus 2.6 to be combined with coarseaggregate of fineness modulus 6.8 for obtaining the aggregates of fineness modulus 5.4, is :

  • a)
    40%

  • b)
    33%

  • c)
    60%

  • d)
    30%

Correct answer is option 'B'. Can you explain this answer?
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The percentage of the fine aggregate of fineness modulus 2.6 to be com...
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The percentage of the fine aggregate of fineness modulus 2.6 to be com...
Given:
Fineness modulus (FM) of fine aggregate = 2.6
Fineness modulus (FM) of coarse aggregate = 6.8
Fineness modulus (FM) of combined aggregates = 5.4

To find:
Percentage of fine aggregate required to be combined with coarse aggregate.

Solution:

1. Formula for fineness modulus:
Fineness modulus (FM) = Summation of cumulative percentage retained on standard sieves / 100
where the standard sieves are 4.75 mm, 2.36 mm, 1.18 mm, 600 microns, 300 microns, 150 microns and 75 microns.

2. Calculation of cumulative percentage retained on standard sieves:
For fine aggregate:
Given FM = 2.6
We can assume that the percentage of material retained on the 600 micron sieve is 100 for FM 2.0 to 3.0.
Therefore, cumulative percentage retained on standard sieves for FM 2.6 can be calculated as follows:

Cumulative percentage retained on 4.75 mm sieve = 0
Cumulative percentage retained on 2.36 mm sieve = 0
Cumulative percentage retained on 1.18 mm sieve = 0
Cumulative percentage retained on 600 micron sieve = 100
Cumulative percentage retained on 300 micron sieve = 88
Cumulative percentage retained on 150 micron sieve = 56
Cumulative percentage retained on 75 micron sieve = 34

For coarse aggregate:
Given FM = 6.8
We can assume that the percentage of material retained on the 4.75 mm sieve is 100 for FM 6.5 to 7.0.
Therefore, cumulative percentage retained on standard sieves for FM 6.8 can be calculated as follows:

Cumulative percentage retained on 4.75 mm sieve = 100
Cumulative percentage retained on 2.36 mm sieve = 97
Cumulative percentage retained on 1.18 mm sieve = 89
Cumulative percentage retained on 600 micron sieve = 61
Cumulative percentage retained on 300 micron sieve = 26
Cumulative percentage retained on 150 micron sieve = 6
Cumulative percentage retained on 75 micron sieve = 1

3. Calculation of combined aggregates:
Given FM of combined aggregates = 5.4
We need to assume a percentage of fine aggregate to be combined with coarse aggregate to obtain FM 5.4.
Let us assume that the percentage of fine aggregate is x.
Therefore, the percentage of coarse aggregate is (100 - x).

Using the formula for fineness modulus, we can calculate the cumulative percentage retained on standard sieves for combined aggregates as follows:

Cumulative percentage retained on 4.75 mm sieve = 100 - x
Cumulative percentage retained on 2.36 mm sieve = 97 - 2.6x/3.2
Cumulative percentage retained on 1.18 mm sieve = 89 - 2.6x/1.8
Cumulative percentage retained on 600 micron sieve = 61 - 2.6x/3.4
Cumulative percentage retained on 300 micron sieve = 26 + 2.6x/12.6
Cumulative percentage retained on 150 micron sieve = 6 + 2.6x/9
Cumulative percentage
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Community Answer
The percentage of the fine aggregate of fineness modulus 2.6 to be com...
fineness modulus of combine mix(z) = 5.4
fineness modulus of coarse aggregate (x) = 6.8
fineness modulus of fine aggregate (y) = 2.8
Percentage of fine aggregate
p = (x-z)/(z-y)×100=(6.8-5.4)/(5.4-2.8)×100
= 53% ⋍ 50%
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The percentage of the fine aggregate of fineness modulus 2.6 to be combined with coarseaggregate of fineness modulus 6.8 for obtaining the aggregates of fineness modulus 5.4, is :a)40%b)33%c)60%d)30%Correct answer is option 'B'. Can you explain this answer?
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