If x, y, z are three sums of money such that y is the simple interest on x, z the simple interest on y for the same time and at the same rate of interest, then which of the following holds true?

y² = zx

S.I. = \(\frac{P\;R\;T}{100}\)

ATQ,

1st: y = \(\frac{x\;R\;T}{100}\)

⇒ \(\frac{R\;T}{100}\) = \(\frac{y}{x}\)  ........(i)

2nd:  z = \(\frac{y\;R\;T}{100}\)

⇒ \(\frac{R\;T}{100}\) = \(\frac{z}{y}\) ..........(ii)

Here, (i) = (ii)

Therefore,

⇒ \(\frac{y}{x}\) = \(\frac{z}{y}\)

⇒ y² = zx