Question

Convert part of the ratio into a percentage: $2:3:5$.

Answer 1

Hint: First, separate the three terms of the ratio and then convert each of them into percentages separately by the formula $P = \dfrac{{{\rm{GV}}}}{{{\rm{TV}}}} \times 100$, where P is a percentage, GV is given value and TV is the total value. Terms of a ratio can be separated by writing them as a multiple of some common terms.

Complete step-by-step solution:
We have, $2:3:5$.
A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
Let $x$ be the common multiple, then the terms will be
$ \Rightarrow 2x,3x,5x$
Therefore, the total value would be
$ \Rightarrow 2x + 3x + 5x = 10x$
We know that,
$P = \dfrac{{GV}}{{TV}} \times 100$
Where,
P is the percentage
GV is given value
TV is the total value
Using this formula, we can write the percentage of $2x$ as,
$ \Rightarrow $ Percentage of $2x = \dfrac{{2x}}{{10x}} \times 100$
Cancel out the common factor,
$ \Rightarrow $ Percentage of $2x = 2 \times 10$
Multiplying the terms, we get
$ \Rightarrow $ Percentage of $2x = 20$
Therefore, the percentage of $2x$ is $20\% $.
Using this formula, we can write the percentage of $3x$ as,
$ \Rightarrow $ Percentage of $3x = \dfrac{{3x}}{{10x}} \times 100$
Cancel out the common factor,
$ \Rightarrow $ Percentage of $3x = 3 \times 10$
Multiplying the terms, we get
$ \Rightarrow $ Percentage of $3x = 30$
Therefore, the percentage of $3x$ is $30\% $.
Using this formula, we can write the percentage of $5x$ as,
$ \Rightarrow $ Percentage of $5x = \dfrac{{5x}}{{10x}} \times 100$
Cancel out the common factor,
$ \Rightarrow $ Percentage of $5x = 5 \times 10$
Multiplying the terms, we get
$ \Rightarrow $ Percentage of $5x = 50$
Therefore, the percentage of $5x$ is $50\% $.

Hence, $20\% ,30\% ,50\% $ are the respective percentage.

Note: We can solve it smartly in short. The sum of all the percentages should be equal to 100.
$ \Rightarrow 2 + 3 + 5 = 10$
Since the sum of the term is 10. So, multiply both sides by 10,
$ \Rightarrow 20 + 30 + 50 = 100$
Hence, $20\% ,30\% ,50\% $ are the respective percentage.