$\mathrm{R}_1=12 \%$
$\mathrm{R}_2=10 \%$
$\mathrm{P}_1=\text { Rs. } 8000$
$\mathrm{P}_2=\text { Rs. } 9100$
Let their amounts be equal in $T$ years.
$\text { Amount }_1=\text { S.I }_1+\mathrm{P}_1$
$=\frac{\mathrm{P}_1 \times \mathrm{I}_1 \times \mathrm{T}}{100}+\mathrm{P}_1$
$=960 \mathrm{~T}+8000$
$\text { Amount }{ }_2=\text { S.I }_2+\mathrm{P}_2$
$=\frac{\mathrm{P}_2 \times \mathrm{r}_2 \times \mathrm{T}}{100}+\mathrm{P}_2$
$=\frac{9100 \times 10 \times \mathrm{T}}{100}+9100$
$=910 \mathrm{~T}+9100$
$\text { Amount }_1=\text { Amount }_2$
$\Rightarrow 960 \mathrm{~T}+8000=910 \mathrm{~T}+9100$
$\Rightarrow 960 \mathrm{~T}-910 \mathrm{~T}=9100-8000$
$\Rightarrow 50 \mathrm{~T}=1100$
$\Rightarrow \mathrm{~T}=22$
Hence, after $22$ years their amounts will be equal.
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