Question

A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?

Answer 1

Let the actual length of bacteria be x cm and the enlarged length of bacteria be y cm, if the photograph is enlarged for 20,000 times.
The given information in the form of a table is as follows.

Length of bacteria (in cm)	5	x	y
Number of times photograph of Bacteria was enlarged	50000	1	20000

The number of times the photograph of bacteria was enlarged, and the length of bacteria are in direct proportion. 
Therefore, we obtain.
\(\frac{5}{50000}=\frac{x}{1}\)
\(⇒ x=\frac{1}{0000} =10^{-4}\)
Let the length of bacteria when the photograph of bacteria is enlarged 20, 000 times be y.
\(\frac{5}{50000}=\frac{y}{20000}\)

\(⇒ y =\frac{5×20000}{50000}=2 cm\)
Hence, the enlarged length of bacteria is 2 cm.