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 = ?

Answer: Option C

Let the amount invested = Rs. P
According to the question,
$$\begin{array}{rl}& \text{P}+\frac{\text{P}\times 10\times 4}{100}=770\\ & \Rightarrow \text{P}+\frac{4\text{P}}{10}=770\\ & \Rightarrow \frac{14\text{P}}{10}=770\\ & \Rightarrow \text{P}=\frac{770\times 10}{14}\\ & \Rightarrow \text{P}=\text{Rs 550}\end{array}$$
Hence, required invested amount = Rs. 550

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