Question

What is the compounded ratio of 10: 30 and 60: 80?

Answer 1

Hint:In this question, we use the concept of compounded ratio. For two or more ratios, if we take antecedent as product of antecedents of the ratios and consequent as product of consequences of the ratios, then the ratio thus formed is called mixed or compound ratio. As, the compound ratio of m: n and p: q is mp: nq.

Complete step-by-step solution:
Now, we have two ratios 10: 30 and 60: 80.
In compounded ratio we have to multiply two or more ratios term wise. Example, the compounded ratio of the two ratios a: b and c: d is the ratio ac: bd.
We can write $10:30 \Rightarrow \dfrac{{10}}{{30}}$ and $60:80 \Rightarrow \dfrac{{60}}{{80}}$
Now, compounded ratio $ = \dfrac{{10}}{{30}} \times \dfrac{{60}}{{80}}$
   $
   \Rightarrow \dfrac{1}{3} \times \dfrac{6}{8} \\
   \Rightarrow \dfrac{6}{{24}} \\
   \Rightarrow \dfrac{1}{4} \\
$
So, the compounded ratio of 10: 30 and 60: 80 is 1:4.

Note: In such types of problems we have to use the definition of compounded ratio and then we have to multiply two ratios term wise (compounded ratio of the two ratios a: b and c: d is the ratio ac: bd). So, after calculation we will get the required answer.