Ex.8.3 Q2 Compairing Quantities - NCERT Maths Class 7

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Question

Convert each part of the ratio to percentage:

(a) \(\begin{align}{ 3:1 }\end{align}\)

(b) \(\begin{align}\text{ 2:3:5 }\end{align}\)

(c) \(\begin{align}\rm{1:4}\end{align}\)

(d) \(\begin{align} \rm{ 1:2:5} \end{align}\)

Text Solution

What is Known?

Different ratios are given

What is Unknown?

Percentage form of the given ratios.

Reasoning:

To convert each part of ratio into percentage we will first divide each part with total of all parts and then multiply it with \(100\) to convert each part into percentage.

Steps:

(a)  In the ration \(3:1,\) total number of parts 

\[\begin{align}&= 3 + 1{\text{ }}\\ &= {\text{ }}4\end{align}\]

Percentage of first  part 

\[\begin{align}&= \frac{{\rm{3}}}{{\rm{4}}} \times {\rm{100}}\\&= 75\%\end{align}\]

 Percentage of second part 

\[\begin{align}&=\frac{{\rm{1}}}{{\rm{4}}} \times {\rm{100}}\\&= 25\% \end{align}\]

(b) In \(2:3:5,\) total number of parts  

\[\begin{align} &= 2 + 3 + 5 \\&= 10\end{align}\]

 Percentge of first part 

\[\begin{align} &=\frac{{\text{2}}}{{{\text{10}}}} \times {\text{100}}\\ &= \,{\text{20% }}\end{align}\]

Percentge of second part 

\[\begin{align}&= \frac{{\text{3}}}{{{\text{10}}}} \times {\text{100}}\\&= 30\%\end{align}\]

Percentge of third part 

\[\begin{align}&=\frac{{\text{5}}}{{{\text{10}}}} \times {\text{100}}\,\\&= 50\% \end{align}\]

(c)  In ratio \(1:4,\) total number of parts 

\[\begin{align}&= 1 + 4 \\ &= 5\end{align}\]

 Percentge of first part 

\[\begin{align}&= \frac{{\text{1}}}{{\text{5}}} \times {\text{100}}\\ &= 20\% \end{align}\]

 Percentge of second part 

\[\begin{align} &= \,\frac{{\text{4}}}{{\text{5}}}{\text{ x 100}}\\\,&= 80\% \end{align}\]

(d)  In ratio \(1:2:5,\) total number of parts 

\[\begin{align} &= 1 +2 + 5 \\&= 8\end{align}\]

Percentge of first  part 

\[\begin{align}&= \frac{{\text{1}}}{{\text{8}}} \times {\text{100}}\,\\&= 12{\text{.5% }}\end{align}\]

 Percentge of  second  part 

\[\begin{align} &= \,\frac{2}{8}{\rm{ \times 100}}\\&=  25\% \end{align}\]

 Percentge of third part 

\[\begin{align}&= \frac{{\text{5}}}{{\text{8}}} \times {\text{100}}\\&= \,{\text{62}}{\text{.5% }}\end{align}\]