Question

What is the compounded ratio of $x:y,y:z,z:w$?
(a) $y:w$
(b) $x:w$
(c) $y:z$
(d) $x:z$

Answer 1

Hint:Compounded ratio means we have to multiply all the ratios and then see what result we are getting. In this problem, we have to find compounded ratio of $x:y,y:z,z:w$ so we have to multiply all the three ratios so multiplication of these ratios in such a way that all the variables which are on the left side of the ratio multiply together and all the variables which are on the right side of the ratio will be multiplied together. So, the compounded ratio of the variables will give $x\left( y \right)\left( z \right):y\left( z \right)\left( w \right)$.

Complete step-by-step answer:
The ratio which we have to compound is:
$x:y,y:z,z:w$
To find the compounded ratio we have to together multiply all the variables which are on the left side of the ratios given in the question and together multiply all the variables which are on the right side of the ratios so the resulting ratio will look like:
$x\left( y \right)\left( z \right):y\left( z \right)\left( w \right)$
As you can see the variable $yz$ is on both the sides of the above ratio so it will be cancelled out and we are remaining with:
$x:w$
From the above solution, the compounded ratio that we have got is $x:w$.
Hence, the correct option is (b).

Note: While finding the compounded ratio, the possible mistake that could happen is you would have wrongly multiplied the left side variables of the ratio. When the ratios are written in a horizontal format you could possibly choose the wrong left side of the variables so it’s better to write the given ratios in the following manner and then multiply.
$\begin{align}
  & x:y \\
 & y:z \\
 & z:w \\
\end{align}$
Writing the given ratios in the above format can possibly reduce the mistake of multiplying the right side of the ratios also in the compounded ratio.