If x, y and 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:

z2 = xy xyz = 1 x2 = yz y2 = xz

y2 = xz

Let rate = R and time = T y = \(\frac{x x R X T}{100}\)  ---(i) z = \(\frac{y x R X T}{100}\)  ---(ii) Dividing eq. (i) and (ii) \(\frac{y}{z}\) = \(\frac{x}{y}\) ⇒ y² = xz