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 \(2 \,\rm{cm.}\)