Question

$x,y,z$ 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 rate. Which of the following is correct?

• A. $xyz=1$
• B. $z^2=xy$
• C. $x^2=yz$
• D. $y^2=zx$

Answer 1

The correct option is D $y^2=zx$

Let rate of interest is $R\%$ and time is $T$ years.

Given, $Y$ is the simple interest of $x$ and $z$ is the simple interest of $y$

Then $y=$ $\frac{x\times R\times T}{100}$

And $z=$ $\frac{Y\times R\times T}{100}$

$\Rightarrow \frac{R\times T}{100}=\frac{z}{y}$

Then $y=$ $x\times \frac{z}{y}\Rightarrow y^2=zx$