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

Hint: To solve this question, we can use the unitary method as for any specific value corresponding to some other value, so that it can be changed to a unit value corresponds to what value, effectively we all can multiply with the unit value with the number of times according to the question.

Complete step-by-step answer:
Given, a photograph of a bacteria enlarged 50,000 times attains a length of 5 cm
We need to find the actual length of the bacteria.
Use, the unitary method now,
50,000 units corresponds to the length of 5 cm.
So,
1 unit corresponds to the length of $\dfrac{5}{{50000}}$ which will be equal to $\dfrac{1}{{10000}} = 0.0001\,{\text{cm}}$.
Therefore, the size of the bacteria is 0.0001 cm.
Now, if the photograph is enlarged 20,000 times, then the size of enlarged length will be,
$20000 \times 0.0001 = 2\,{\text{cm}}$, therefore, when the photograph is enlarged 20,000 times its length attains 2 cm.

Note: This question can also be solved with the help of the concept of direct proportion, It can be observed that when the value of something is increasing or decreasing, simultaneously the associated value also increases or decreases in such a way that the ratio these two quantities does not change; it remains constant. We say that these two quantities are in direct proportion.