Question : If $x, y,$ and $z$ are three sums 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 we have:
Option 1: $z^{2}=xy$
Option 2: $xyz=1$
Option 3: $x^{2}=yz$
Option 4: $y^{2}=zx$

Question

Question : If $x, y,$ and $z$ are three sums 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 we have:

Option 1: $z^{2}=xy$

Option 2: $xyz=1$

Option 3: $x^{2}=yz$

Option 4: $y^{2}=zx$

Team Careers360 · Accepted Answer

Correct Answer: $y^{2}=zx$

Solution : Let the time be $t$ years and the rate of interest be $R$.
We know, Simple interest = $\frac{ ext{Principal × Rate × Time}}{100}$
According to the question,
Case(I): $y=\frac{x imes R imes t}{100}$-------------(i)
Case(II): $z=\frac{y imes R imes t}{100}$------------(ii)
By dividing equation (i) by equation (ii), we get,
$\frac{y}{z}=\frac{x imes R imes t}{y imes R imes t}$
$⇒y^{2}=zx$
Hence, the correct answer is $y^{2}=zx$.

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Question : If x,y, and z are three sums 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 we have:Option 1: z2=xyOption 2: xyz=1Option 3: x2=yzOption 4: y2=zx

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Question : If $x, y,$ and $z$ are three sums 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 we have:
Option 1: $z^{2} = x y$
Option 2: $x y z = 1$
Option 3: $x^{2} = y z$
Option 4: $y^{2} = z x$