Answer
The new value is $25$
Work Step by Step
$M=\frac{∑X}{N}$
One of the scores will be changed. Since, the position of this score in the sum makes no difference, let's name this score as $X_9$.
Before:
There are 9 scores whose mean is $20$:
$20=\frac{X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+X_9}{9}$
$X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+X_9=20\times9=180$
$X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+7=180$
$X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8=173$
After:
There are 9 scores whose mean is $22$:
$22=\frac{X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+X_9}{9}$
$X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+X_9=198$
$(X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8)+X_9=198$
$173+X_9=198$
$X_9=25$
