Question

If \[p\] is \[128\% \] of \[r\], \[q\] is \[96\% \] of \[r\] and \[r\] is \[250\% \] of \[s\]. Find the ratio of \[p:q:s\] in lowest terms.

Answer 1

Hint:
Here we will use the concept of ratio. Firstly we will find the value of \[p,q,s\] in the common terms i.e. \[r\]. Then we will put their value in the ratio form. Then we will make it in the lowest form by canceling out the common factors from the ratio equation.

Complete step by step solution:
It is given that \[p\] is \[128\% \] of \[r\]. Therefore, we get
\[p = \dfrac{{128}}{{100}}r\]
It is given that \[q\] is \[96\% \] of \[r\]. Therefore, we get
\[q = \dfrac{{96}}{{100}}r\]
It is given that \[r\] is \[250\% \] of \[s\]. Therefore, we get
\[r = \dfrac{{250}}{{100}}s\]
Now we will simplify this above equation to get the value of \[s\]. Therefore, we get
\[s = \dfrac{{100}}{{250}}r\]
Now we will find the value of the ratio \[p:q:s\] by putting the value of \[p,q,s\] in it. Therefore, we get
\[ \Rightarrow p:q:s::\dfrac{{128}}{{100}}r:\dfrac{{96}}{{100}}r:\dfrac{{100}}{{250}}r\]
Now we will cancel out all the common factors in the ration. Therefore, we get
\[ \Rightarrow p:q:s::\dfrac{{128}}{{10}}:\dfrac{{96}}{{10}}:\dfrac{{100}}{{25}}\]
\[ \Rightarrow p:q:s::\dfrac{{128}}{2}:\dfrac{{96}}{2}:\dfrac{{100}}{5}\]
\[ \Rightarrow p:q:s::64:48:20\]
Now we will make this in the least form by dividing it by 4 as all the numbers are the multiple of 4. Therefore, we get
\[ \Rightarrow p:q:s::16:12:5\]

Hence, the ratio of \[p:q:s\] in lowest terms is \[16:12:5\].

Note:
Here we should know that ratio is a similar concept to the fraction. The ratio is the form that represents how many times one number is to another number. It also represents the weightage of the given variable in some lowest terms. It is generally used when we have to compare some variables with large values. A ratio can be written for two or more than two items or numbers. We should note that for making the ratio in the lowest terms we have to cancel out all the common terms from the ratio equation.