Question

If \[\dfrac{a}{b} = 2\] ,what is the value of \[\dfrac{{4b}}{a}\] ?

Answer 1

Hint: In this question, we have given \[\dfrac{a}{b} = 2\] and we are asked to find out the value of \[\dfrac{{4b}}{a}\] .So, in order to solve this question, we will first find out the value of \[a\] from the given expression i.e., \[\dfrac{a}{b} = 2\] .After that we will substitute the value of \[a\] in \[\dfrac{{4b}}{a}\] and find out the required value of \[\dfrac{{4b}}{a}\]

Complete step-by-step answer:
Here, it is given that
\[\dfrac{a}{b} = 2\]
And we have to find out the value of \[\dfrac{{4b}}{a}\]
So, first of all let the given expression as equation \[\left( 1 \right)\]
i.e., \[\dfrac{a}{b} = 2{\text{ }} - - - \left( 1 \right)\]
Now, from equation \[\left( 1 \right)\] we will find the value of \[a\]
So, on multiplying equation \[\left( 1 \right)\] by \[b\] on both sides, we get
\[\dfrac{a}{b} \times b = 2 \times b\]
Now, on cancelling \[b\] from the left-hand side of the above expression, we get
\[a = 2b\]
Thus, we get the value of \[a\] as \[2b\]
Now, to find out the value of \[\dfrac{{4b}}{a}\] ,all we have to do is substitute the value of \[a\]
Therefore, we get
\[\dfrac{{4b}}{a} = \dfrac{{4b}}{{2b}}\]
Now, on cancelling \[b\] from both numerator and denominator of the above expression, we get
\[\dfrac{{4b}}{a} = \dfrac{4}{2}\]
Now, on dividing \[4\] by \[2\] we get,
\[\dfrac{{4b}}{a} = 2\]
Thus, we get the value of \[\dfrac{{4b}}{a}\] equals to \[2\]
Hence, we get the required result.
i.e., If \[\dfrac{a}{b} = 2\] ,then the value of \[\dfrac{{4b}}{a} = 2\]
So, the correct answer is “2”.

Note: This question can also be solved by an alternative method. That is,
As it is given that, \[\dfrac{a}{b} = 2\]
We can rewrite the above expression as \[\dfrac{a}{b} = \dfrac{2}{1}\]
which can also be written as \[\dfrac{b}{a} = \dfrac{1}{2}{\text{ }} - - - \left( 1 \right)\]
Now, we have to find out the value of \[\dfrac{{4b}}{a}\]
So, \[\dfrac{{4b}}{a}\] can also be written as \[4 \times \dfrac{b}{a}{\text{ }} - - - \left( 2 \right)\]
Now, on substituting the value of \[\dfrac{b}{a}\] from the equation \[\left( 1 \right)\] in the equation \[\left( 2 \right)\] we get,
\[\dfrac{{4b}}{a} = 4 \times \dfrac{1}{2}\]
On dividing \[4\] by \[2\] we get,
\[ \Rightarrow \dfrac{{4b}}{a} = 2\]
Thus, we get the value of \[\dfrac{{4b}}{a}\] equals to \[2\]
Hence, we get the required result.