Question

(b) 2:5:9
(a) 2:3:5
6. Convert each part of the ratio into percentage.​

Answer 1

★ How to do :-

Here, we are given with two ratios in which we are asked to convert each part of the ratio to the percentage form. Percentage means 'per hundred'. We should convert them into percentage form by using the formula given below. So, first we should add all the digits given in the ratio and then we should take the part of ratio as numerator and the sum of all digits as denominator and then use the given formula. So, let's solve!!

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➤ Solution (1) :-

${\tt \leadsto 2 + 5 + 9}$

${\tt \leadsto 16}$

Now,

Percentage of first part :-

${\tt \leadsto \dfrac{2}{16} \times 100}$

${\tt \leadsto \cancel \dfrac{2}{16} \times 100 = \dfrac{1}{8} \times 100}$

${\tt \leadsto \dfrac{1 \times 100}{8} = \dfrac{100}{8}}$

${\tt \leadsto \cancel \dfrac{100}{8} = \orange{\boxed{\tt 12.5 \bf\%}}}$

Percentage of second part :-

${\tt \leadsto \dfrac{5}{16} \times 100}$

${\tt \leadsto \dfrac{5}{\cancel{16}} \times \cancel{100} = \dfrac{5}{4} \times 25}$

${\tt \leadsto \dfrac{5 \times 25}{4} = \dfrac{125}{4}}$

${\tt \leadsto \cancel \dfrac{125}{4} = \orange{\boxed{\tt 31.25 \bf\%}}}$

Percentage of third part :-

${\tt \leadsto \dfrac{9}{16} \times 100}$

${\tt \leadsto \dfrac{9}{\cancel{16}} \times \cancel{100} = \dfrac{9}{4} \times 25}$

${\tt \leadsto \dfrac{9 \times 25}{4} = \dfrac{225}{4}}$

${\tt \leadsto \cancel \dfrac{225}{4} = \orange{\boxed{\tt 56.25 \bf\%}}}$

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➤ Solution (2) :-

${\tt \leadsto 2 + 3 + 5}$

${\tt \leadsto 10}$

Now,

Percentage of first part :-

${\tt \leadsto \dfrac{2}{10} \times 100}$

${\tt \leadsto \cancel \dfrac{2}{10} \times 100 = \dfrac{1}{5} \times 100}$

${\tt \leadsto \dfrac{1 \times 100}{5} = \dfrac{100}{5}}$

${\tt \leadsto \cancel \dfrac{100}{5} = \orange{\boxed{\tt 20 \bf\%}}}$

Percentage of second part :-

${\tt \leadsto \dfrac{3}{10} \times 100}$

${\tt \leadsto \dfrac{3}{\cancel{10}} \times \cancel{100} = \dfrac{3}{1} \times 10}$

${\tt \leadsto \dfrac{3 \times 10}{1} = \dfrac{30}{1}}$

${\tt \leadsto \cancel \dfrac{30}{1} = \orange{\boxed{\tt 30 \bf\%}}}$

Percentage of third part :-

${\tt \leadsto \dfrac{5}{10} \times 100}$

${\tt \leadsto \cancel \dfrac{5}{10} \times 100 = \dfrac{1}{2} \times 100}$

${\tt \leadsto \dfrac{1 \times 100}{2} = \dfrac{100}{2}}$

${\tt \leadsto \cancel \dfrac{100}{2} = \orange{\boxed{\tt 50 \bf\%}}}$

Hence solved !!

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The formula applied to calculate the percentage is

${\sf \longrightarrow \dfrac{Obtained \: value}{Total \: value} \times 100}$