If $x, y, z$ are three sums of money such that $y$ is the simple interest on $x, z$ is the simple interest on $y$ for the same time and at the same rate of interest, then we have
(a)$x^{2}=y z$
(b)$y^{2}=x z$
(c)$z^{2}=x y$
(d)$x y z=1$
Answer
Answer (as printed): B
Explanation
Let time be $T$ years and rate be $R \%$ p.a. Then, $y$ is the S.I. on $x \Rightarrow \frac{x R T}{100}=y$ And, $z$ is the S.I. on $y \Rightarrow \frac{y R T}{100}=z \Rightarrow y=\frac{100 z}{R T}$From (i) and (ii) we have: $\frac{x R T}{100}=\frac{100 z}{R T}$ $\Rightarrow \quad \frac{x R^{2} T^{2}}{(100)^{2}}=z \Rightarrow \frac{y^{2}}{x} z \Rightarrow y^{2}=x z$.
Explanation as extracted from the printed page; notation may be imperfect.