Question

Mark (✓) against the correct answer
x, y and z are three sums of money such that y is the simple interest on x and z is the simple interest on y for the same time and same rate. Which of the following is correct?

(a) xyz = 1
(b) z² = xy
(c) x² = yz
(d) y² = zx

Answer 1

(d) y² = zx

$$\begin{gathered} \begin{array}{l}y=\text{S.I. on}x=\frac{x\times \text{R×T}}{100}...\left(\mathrm{i}\right)\end{array} \\ z=\text{S.I. on}y=\frac{y\times \text{R×T}}{100}...\left(\mathrm{ii}\right) \\ \mathrm{Dividing}\mathrm{equation}\left(\mathrm{i}\right)\mathrm{by}\left(\mathrm{ii}\right): \\ \Rightarrow \frac{\mathrm{y}}{\mathrm{z}}=\left(\frac{\mathrm{x}\times \text{R×T}}{100}\times \frac{100}{\mathrm{y}\times \text{R×T}}\right) \\ \Rightarrow \frac{\mathrm{y}}{\mathrm{z}}=\frac{\mathrm{x}}{\mathrm{y}} \\ \Rightarrow {\mathrm{y}}^2=\mathrm{xz} \end{gathered}$$