Answer
The added score: $X_{10}=3$
Work Step by Step
$M=\frac{∑X}{N}$
There are 9 scores whose mean is $13$:
$13=\frac{X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+X_9}{9}$
$X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+X_9=13\times9=117$
A new score is added ($X_{10}$). Now, there are 10 scores whose mean is $12$:
$12=\frac{X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+X_9+X_{10}}{10}$
$X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+X_9+X_{10}=12\times10=120$
$(X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+X_9)+X_{10}=120$
$117+X_{10}=120$
$X_{10}=3$
