The purchase cost of a PFR of $10$ m$^3$ volume was Rs$\mathrm{.}5,00,000$ in $2006.$ What will be the $6$ th cost of a similar PFR of $20$ m$^3$ volume in the year $2020.$ Assume rule for scaling. The $10$ cost index in $2006$ is $420\mathrm{.}2.$ The projected cost index in $2020$ is $720\mathrm{.}2.$

a$)$ Rs$.1296927\mathrm{.}9$

b$)$ Rs$.1238927\mathrm{.}9$

c$)$ Rs$.1298927\mathrm{.}9$

d$)$ Rs$.1278927\mathrm{.}9$