# Ex.13.1 Q5 Direct and Inverse Proportions Solution - NCERT Maths Class 8

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## Question

A photograph of a bacteria is enlarged $$50,000$$ times attains a length of $$​​5 ​​\rm{cm}$$ as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged $$20,000$$ times only, what would be its enlarged length?

## Text Solution

What is Known?

Bacteria enlarged $$50,000$$ times attain a length of $$5 \,\rm{cm.}$$

What is Unknown?

Actual length of the bacteria

if $$20,000$$ times enlarged what will be the length of the bacteria?

Reasoning:

Two numbers $$x$$ and $$y$$ are said in direct proportion if,

\begin{align}\frac{x}{y}=k,\quad x=y\,k\end{align}

Where $$k$$ is a constant.

Steps:

\begin{align} \text{Actual length,}\ l&=\frac{{{y}_{1}}}{{{x}_{1}}} \\ l&=\frac{5}{50000} \\ l&=0.0001\ \rm{cm} \\ \end{align}

 ${{\bf{Number \;of\; times\; enlarged}}}$ ${{\bf{Length \;attained}}}$ ${{x_1} = {\rm{50,000}}}$ ${{y_{\rm{1}}} = {\rm{5}}}$ ${{x_2} = {\rm{20,000}}}$ ${{y_{\rm{2}}} = {\rm{?}}}$

The number of times enlarged is directly proportional to the length attained.

Actual length $$= 0.0001 \,\rm{cm}$$

Enlarged length will be $$2 \,\rm{cm.}$$

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