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The area of the plan of an old survey plotted to a scale of $10$ metres to $1$ cm measures now as $100\mathrm{.}2$ sq$.$ cm as found by a planimeter. The plan is found to have shrunk so that a line originally $10$ cm long now measures $9\mathrm{.}7$ cm only.

Find

$($i$)$the shrunk scale, $($ii$)$ true area of the survey.