Question $3$

$($a$)$ The table below shows the field data for a line of levels between two stations A and $G,150m$ apart. The leveling was begun from Benchmark $1$ near A and was closed on Benchmark $2$ near $G.$ After completion of the leveling, it was found that one of the readings of station $D$ has accidentally not been recorded. Using the available data, calculate the missing data and reduce the level of each station.

Table $3$

$(18$ marks$)$

$\backslash$table$[[$Station$,\backslash$table$[[$Chainage$],[($m$)]],\backslash$table$[[$BS$],[($m$)]],\backslash$table$[[$IS$],[($m$)]],\backslash$table$[[$FS$],[($m$)]],\backslash$table$[[$Reduced$],[$Level $($m$)],[($m$)]]],[$BM$1,--,0\mathrm{.}25,,,99\mathrm{.}89],[$A$,0,,1\mathrm{.}54,,],[$B$,25,0\mathrm{.}72,,1\mathrm{.}20,],[$C$,50,,0\mathrm{.}43,,],[$D$,75,2\mathrm{.}42,,??,],[$E$,100,,1\mathrm{.}05,,],[$F$,125,2\mathrm{.}23,,2\mathrm{.}15,],[$G$,150,,1\mathrm{.}63,,101\mathrm{.}43]]$

$($b$)$ From Station A$,$ a trench is to be excavated with its base rising at a gradient of $1$ in $200$ towards station $G.$ If the base level at station $A$ is $1\mathrm{.}5m$ below the ground surface, determine the depth of excavation at each station.

$(7$ marks$)$