A converging$-$diverging nozzle with an area ratio $($exit to throat$)$ of $3\mathrm{.}0$ exhausts air from a large high$-$pressure reservoir to a region of back pressure Pb$.$ Under a certain operating condition, a normal shock is observed in the nozzle at an area equal to $2\mathrm{.}2$ times the throat area. Calculate the percent decrease in back pressure necessary to rid the nozzle of the normal shock.

Answer: $\%30$