Multiple choice

If $X, Y, Z$ are the three sums of money such that $Y$ is a simple interest on $X$ and $Z$ is a simple interest on $Y$ for same time and rate, then

  1. ${ X }^{ 2 }=YZ\quad $
  2. ${ Y }^{ 2 }=ZX\quad $
  3. ${ Z }^{ 2 }=XY$
  4. $XYZ=1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Y = X * r * t / 100 and Z = Y * r * t / 100. Thus, Z/Y = Y/X, which implies Y^2 = ZX.

AI explanation

Since Y is the simple interest on X, we write Y = (X * R * T) / 100. Because Z is the simple interest on Y for the same rate and time, Z = (Y * R * T) / 100. Substituting the first equation into the second gives Z = (Y * (Y / X)), which simplifies to Z = Y^2 / X. Rearranging this relationship yields Y^2 = ZX.

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