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?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → y2 = zx
Simple interest is \(\frac{P\times R\times T}{100}\). With the same rate and the same time, the factor \(\frac{RT}{100}\) is the same for both sums; call it \(k\). So each interest is \(k\) times its principal.
\(y=kx\), so \(\displaystyle k=\frac{y}{x}\)
\(z=ky\), so \(\displaystyle k=\frac{z}{y}\)
Both give the same \(k\): \(\displaystyle \frac{y}{x}=\frac{z}{y}\), so \(y^2=zx\)