# 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}

Video Solution
Comparing Quantities
Ex 8.3 | Question 2

## 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}

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