Question

If $x:y::y:z$ then the correct statement is:
A. xy = yz
B. \[{{y}^{2}}=xz\]
C. xyz = x
D. zy = x

Answer 1

Hint: For the above question we will have to know the ratio and proportion. A ratio is a comparison between two values expressed as a quotient and a proportion is an equation stating that two ratios are equal. We will just cross multiply it to get the required expression.

Complete Step-by-Step solution:
In the above question we have been given that x, y and y, z are in a ratio and they are in a proportion which means their ratios are equal.
So, we can write the given ratios as follows:
\[\dfrac{x}{y}=\dfrac{y}{z}\]
Now, we will cross multiply the above ratios and we get:
\[\begin{align}
  & \dfrac{x}{y}=\dfrac{y}{z} \\
 & \Rightarrow x\times z=y\times y \\
 & \Rightarrow {{y}^{2}}=xz \\
\end{align}\]
Therefore, the correct option of the above question is option B.

Note: The ratio can be written as a : b or as a fraction a/b and we say the ratio is a to b. Just remember the concept of solving the proportion which I have already mentioned in the hint as it will help you a lot in these types of questions.