From given circuit, if $i=$ circuit current, then

$V=i R_{ eq } \Rightarrow i=\frac{10}{4}=2.5 \,A$

So, power dissipated by circuit is

$P=i^2 R=(2.5)^2 \times 1=\frac{25}{4} W$

When $1 \,\Omega$ resistor is replaced by a $9 \,\Omega$ resistor, then power dissipated in $9\, \Omega$ resistor is

$P^{\prime}=\left(\frac{10}{12}\right)^2 \times(9)$

$=\frac{100 \times 9}{12 \times 12}=\frac{25}{4} \,W$

So, $P^{\prime}=P$