A liquid limit test conducted on a soll sample in the cup device gave the following results:

$\backslash$table$[[$Number of blows,$10,19,23,27,40],[$Water content $(\%),60\mathrm{.}00,45\mathrm{.}20,39\mathrm{.}80,36\mathrm{.}50,25\mathrm{.}20]]$

Two determinations for the plastic limit gave water content of $20\mathrm{.}30\%$ and $20\mathrm{.}80\%.$

Determine :

$($i$)$ The liquid limit and plastic limit

$($ii$)$ The plasticity index

$($iii$)$ The liquidity index if the natural water content is $27\mathrm{.}40\%$ and

$($iv$)$ The void ratio at the liquid IImit, if the $sp.$ gravity, $Gs=2\mathrm{.}7.$ If the soll were to be londent to failure, would you expect brittle failure?