Question

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

Answer 1

Hint: Separate the three terms of the ratio and then convert each of them into percentage separately. Terms of a ratio can be separated by writing them as a multiple of some common term.

Complete step-by-step answer:
We have, $ 2:3:5 $ .
Let $ x $ be the common multiple, then the terms will be
 $ 2x,3x,5x $
Therefore, total value would be
 $ 2x + 3x + 5x = 10x $
We know that,
 $ P = \dfrac{{GV}}{{TV}} \times 100 $
Where,
P is percentage
GV is given value
TV is total value
Using this formula, we can write
Percentage of $ 2x = \dfrac{{2x}}{{10x}} \times 100 $
 $ = 2 \times 10 $
 $ = 20 $
Therefore, the percentage of $ 2x $ is $ 20\% $
Similarly,
Percentage of $ 3x = \dfrac{{3x}}{{10x}} \times 100 $
 $ = 3 \times 10 $
 $ = 30 $
Therefore, the percentage of $ 3x $ is $ 30\% $
Similarly,
Percentage of $ 5x = \dfrac{{5x}}{{10x}} \times 100 $
 $ = 5 \times 10 $
 $ = 50 $
Therefore, the percentage of $ 5x $ is $ 50\% $

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