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 $x:y={\displaystyle \frac{x}{y}}$ then we multiply it by 100 and put the percentage sign.
So, in (a) part we have,
3 : 1
So $3:1={\displaystyle \frac{3}{1}}$
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 ${\displaystyle \frac{1}{4}}$ .
Now we will multiply it by 100 to obtain the percentage.
Therefore, ${\displaystyle \frac{100}{4}}=25$ .
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,
$1x+2x+5x=100$
$7x=100$
$x={\displaystyle \frac{100}{7}}$
Therefore, we can write 1 : 2 : 5 as ${\displaystyle \frac{100}{7}}$ by substituting the value of $x={\displaystyle \frac{100}{7}}$ in 1x, 2x, 5x respectively as ${\displaystyle \frac{200}{7}}$ and ${\displaystyle \frac{500}{7}}$.

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 ${\displaystyle \frac{x}{y}}$ and to find its percentage we multiply it by 100 as ${\displaystyle \frac{x}{y}}\times 100$.