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

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