Consider three different processors $P1,P2,$ and $P3$ executing the same instruction set. $P1$ has a $3GHz$ clock rate and a CPI of $1\mathrm{.}5.$ P$2$ has a $2\mathrm{.}5GHz$ clock rate and a CPI of $1\mathrm{.}0.$ P$3$ has a $4\mathrm{.}0GHz$ clock rate and has a CPI of $2\mathrm{.}2.$

$($a$)$ If the processor P$1$ execute a program in $10$ seconds, find the number of cycles and the number of instructions.

$($b$)$ We are trying to reduce the execution time by $20\%$ for P$1,$ but this leads to an increase of $30\%$ in the CPI. What clock rate should we have to get this time reduction for P$1?$