Question

Convert each part of ratio to percentage:
(A). 3 : 1
(B). 2 :3 : 5
(C). 1 : 4
(D). 1 : 2 : 5

Answer 1

Hint: We will be using the concepts of ratio and proportion to solve the problem also we will be using percentage concept to convert the ratio to percentage.

Complete step-by-step solution -
Now, we have to convert ratio to percentage. So we know that to convert a ratio to percentage, we will first convert it to fraction as $x:y=\dfrac{x}{y}$ then we multiply it by 100 and put the percentage sign.
So, in (a) part we have,
3 : 1
So $3:1=\dfrac{3}{1}$
Now we multiply it by 100. Therefore,
$ =3\times 100% \\ $
$ =300% \\ $
Now, in (b) part we have a ratio as 2 : 3 : 5. So, we will let the percentage of each be 2x, 3x, 5x. Now, we know the total percentage is 100%. Therefore,
$ 2x+3x+5x=100% \\ $
$ 10x=100% \\ $
$ x=10% \\ $
Therefore, we can write 2 : 3 : 5 as 20%, 30%, 50% by substituting the value of $x=10%$ in 2x, 3x, 5x.
Now in (c) part we have the ratio as 1 : 4. Now, we will represent this as the rational number as $\dfrac{1}{4}$ .
Now we will multiply it by 100 to obtain the percentage.
Therefore, $\dfrac{100}{4}=25%$ .
So, 1 : 4 in percentage is 25%.
Now in (d) part we have the ratio as 1 : 2 : 5. So, we will let the percentage of each be 1x, 2x, 5x. Now we know the total percentage is 100%. Therefore,
$ 1x+2x+5x=100% \\ $
$ 7x=100% \\ $
$ x=\dfrac{100}{7}% \\ $
Therefore, we can write 1 : 2 : 5 as $\dfrac{100}{7}%,\dfrac{200}{7}%,\dfrac{500}{7}%$ by substituting the value of $x=\dfrac{100}{7}%$ in 1x, 2x, 5x respectively as $\dfrac{200}{7}$ and $\dfrac{500}{7}$.

Note: To solve these types of questions one must know the concepts of ratio and proportion. One must know that if ratio is x:y then in rational can be represented as $\dfrac{x}{y}$ and to find its percentage we multiply it by 100 as $\dfrac{x}{y}\times 100%$.