$\rightarrow$ Suppose $1$ worker does $1$ unit of work in $1$ hour.
$\rightarrow$ So everyday a worker does $8$ units of work.
$\rightarrow$ Work done by $80$ such workers in $90$ days = ($90*80*8$) units = $57600$ units
$\rightarrow$ This $57600$ units of work is $\frac{2}{7}$th of the total work.
$\therefore$ Remaining work = $\frac{5}{7}$th of the total work = $57600 *\frac{7}{2}*\frac{5}{7}$ = $144000$ units
and Remaining days = $180-90$ = $90$ days
$\rightarrow$ Suppose ($80+x$) workers completes the remaining work in the remaining $90$ days
$\rightarrow$ Here $x$ extra workers and each one of them do $10$ units of work everyday for the remaining $90$ days.
$\rightarrow$The other $80$ workers, each of them do $8$ units of work everyday for the remaining $90$ days.
$\rightarrow$ Togather they have to complete $144000$ units of work in $90$ days
$\Rightarrow$ $(80*8*90) + (x*10*90) = 144000$
$\Rightarrow$ $(64*900) + (x*900) = 14400$
$\Rightarrow$ $64+ x=160$
$\Rightarrow$ $x=160-64 =96$
$\therefore$ We need $96$ extra workers to complete the remaining work in $90$ days.