Answer: Option C
Let the amount invested = Rs. P
According to the question,
$$\eqalign{
& {\text{P}} + \frac{{{\text{P}} \times 10 \times 4}}{{100}} = 770 \cr
& \Rightarrow {\text{P}} + \frac{{4{\text{P}}}}{{10}} = 770 \cr
& \Rightarrow \frac{{14{\text{P}}}}{{10}} = 770 \cr
& \Rightarrow {\text{P}} = \frac{{770 \times 10}}{{14}} \cr
& \Rightarrow {\text{P}} = {\text{Rs 550}} \cr} $$
Hence, required invested amount = Rs. 550
Alternate
$$\eqalign{
& {\text{10}}\% {\text{ = }}\frac{{1 \to {\text{Interest}}}}{{10 \to {\text{Principal}}}} \cr
& {\text{Interest in 4 years}} \cr
& {\text{ = 1}} \times {\text{4}} \cr
& = {\text{4}} \cr
& {\text{Amount = }} \cr
& = \left( {{\text{Interest + Principal}}} \right) \cr
& = 4 + 10 \cr
& = 14 \cr
& {\text{According to the question,}} \cr
& {\text{14 units = 770}} \cr
& {\text{1 unit = }}\frac{{770}}{{14}} \cr
& {\text{10 units = }}\frac{{770}}{{14}} \times {\text{10}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 550 }} \cr
& {\text{The amount invested}} \cr
& {\text{ = Rs}}{\text{. 550}} \cr} $$