Rajan bought a watch for Rs 1870 including VAT at 10%.

Let the original price be Rs $x$.

VAT $=10 \%$ of Rs $x$

$=\operatorname{Rs}\left(x \times \frac{10}{100}\right)$

$=\operatorname{Rs} \frac{x}{10}$

$\therefore$ Price including $\mathrm{VAT}=\mathrm{Rs}\left(\mathrm{x}+\frac{\mathrm{x}}{10}\right)$

$=$ Rs. $\frac{11 x}{10}$

$\therefore \frac{11 x}{10}=1870$

$\Rightarrow x=\left(1870 \times \frac{10}{11}\right)$

$\Rightarrow x=1700$

$\therefore$ The original price of the watch is Rs 1,700 .