Question

What is the compound ratio of 3:5 , 7:9 and 15:28 ?
(a). 1:4
(b). 5:7
(c). 9:8
(d). 3:7

Answer 1

Hint: First we will look at the definition of compound ratio and then we will use that definition to find the asked compound ratio by first writing all the numbers in fraction and then multiplying them and then we are going to cancel the common terms in numerator and denominator and then after rearranging them we will get the final answer.


Complete step-by-step solution -

Let’s start solving the question by first stating the definition of compound ratio,
Compounded Ratio: When we compound two or more ratios with each other through product or multiplication, the result is simply a compound ratio. Thus, the product of two or more ratios, like ab:cd is a ratio compounded of the simple ratios a:c and b:d.

Now as we have given the definition now we are going to solve this question.
Let’s now write the ratio in fraction and then multiply it,
After multiplying all three of them we get,
$\begin{align}
  & \dfrac{3}{5}\times \dfrac{7}{9}\times \dfrac{15}{28} \\
 & =\dfrac{45\times 7}{45\times 28} \\
 & =\dfrac{1}{4} \\
\end{align}$
Hence we have found the value of compound ratio.
Hence option (a) is the correct answer.


Note: We have used the definition of compound ratio and then converted them into fraction and then multiply it. Students might get stuck in the meaning of compound ratio, that’s why it’s definition is very important and the steps that we have used is the shortest way to solve this question.