Jhon invested a sum of money at an annual simple interest rate of 10%. At the end of four years the amount invested plus interest earned was Rs. 770. The amount invested was = ?

Solution(By Examveda Team)

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
$$\eqalign{ & {\text{10}}\% {\text{ = }}\frac{{1 \to {\text{Interest}}}}{{10 \to {\text{Principal}}}} \cr & {\text{Interest in 4 years}} \cr & {\text{ = 1}} \times {\text{4}} \cr & = {\text{4}} \cr & {\text{Amount = }} \cr & = \left( {{\text{Interest + Principal}}} \right) \cr & = 4 + 10 \cr & = 14 \cr & {\text{According to the question,}} \cr & {\text{14 units = 770}} \cr & {\text{1 unit = }}\frac{{770}}{{14}} \cr & {\text{10 units = }}\frac{{770}}{{14}} \times {\text{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 550 }} \cr & {\text{The amount invested}} \cr & {\text{ = Rs}}{\text{. 550}} \cr} $$