If x, y, z are three sum of money such that y is the simple interest on x and z is the simple interest on y for the same time and at the same rate of interest, then what is the relation between x, y, z we have = ?

Answer: Option D

Let the time is 't' years and the rate of interest is R%
According to the question,
$$\begin{array}{rl}& \mathbf{Case}(\mathbf{I}):\\ & y=\frac{x\times \text{R}\times \text{t}}{100}.....(i)\\ & \mathbf{Case}(\mathbf{II}):\\ & z=\frac{y\times \text{R}\times \text{t}}{100}.....(ii)\end{array}$$
By dividing equation (i) by equation (ii)
$$\begin{array}{rl}& \frac{y}{z}=\frac{x\times \text{R}\times \text{t}}{y\times \text{R}\times \text{t}}\\ & \Rightarrow y^2=zx\end{array}$$