As, force $F=m a$

$\Rightarrow \frac{\Delta F}{F}=\frac{\Delta m}{m}+\frac{\Delta a}{a} \Rightarrow \frac{\Delta m}{m}=\frac{\Delta F}{F}-\frac{\Delta a}{a}$

$\Rightarrow \frac{\Delta m}{m}=\left(\frac{\pm 0.2}{10}\right)-\left(\frac{\pm 0.01}{1}\right)$

So, $\left(\frac{\Delta m}{m}\right)_{\max }=\frac{0.2}{10}+\frac{0.01}{1}=0.03$

Maximum error in mass occurs when error in force and acceleration are of different signs.

So, $\Delta m=0.03 \times m=0.03 \times 10 \Rightarrow \Delta m=0.3\, kg$

Hence, mass of object is $m=10 \pm 0.3 \,kg$.