In a highway I in $50$ elevation gradient meets $1$ in $400$ fall gradient at a chainage of

$1200$m and at a reduced level of $150\mathrm{.}00$m$.$ If the sight distance be $300$m$,$ determine

the Length of the vertical curve and the reduced Levels of the Tangent Points and

the Apex of the curve, using a $30$m Chain. Assuming the Eye Level of a Driver to

be $1\mathrm{.}2$m above the Road Surface and the height of the obstacle to be $0\mathrm{.}1$m