Question $9(20\%)$

Referring to table below, Mix No$.1$ was designed to produce a $50mm$ slump without water reducer. Mixes Nos. $2-3$ are trial mixes with water reducer. All mixes have the same amounts of aggregate and cement, different amounts of mixing water. If the compressive strength at $28$ days $(f_c)$ follows the results shown in the graph below, determine the following items:

a$.$ Water$-$cement ratio of each mix.

b$.fc$ of each mix using the graph provided below.

c$.$ Comment on the effect of adding water reducer to the mix and discuss how to make use of it to increase the compressive strength of concrete.

Assume all aggregates are in SSD moisture state.

$\backslash$table$[[$Mix No$.,$Aggregate, kg$,$Cement, kg$,$Water, $kg,\backslash$table$[[$Water$],[$Reducer$]],$Slump, mm$],[1,45\mathrm{.}5,10\mathrm{.}5,5\mathrm{.}23,$No$,50],[2,45\mathrm{.}5,10\mathrm{.}5,5\mathrm{.}23,$Yes,$175],[3,45\mathrm{.}5,10\mathrm{.}5,4\mathrm{.}32,$Yes,$100],[,,,,,]]$