If x is the simple interest on y and y is the simple interest on z, the rate per cent and the time being the same in both cases, what is the relation between x, y and z?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(y^2=xz\)
Simple interest is \(\frac{PRT}{100}\). With the same rate R and time T in both cases, the interest is the same fixed fraction \(\frac{RT}{100}\) of the principal each time.
Interest on y is x: \(\displaystyle x=\frac{y\,RT}{100}\) (1)
Interest on z is y: \(\displaystyle y=\frac{z\,RT}{100}\) (2)
Dividing (1) by (2), \(\frac{RT}{100}\) cancels: \(\displaystyle \frac{x}{y}=\frac{y}{z}\)
\(y^2=xz\)