In a certain pond, 50 fish were caught, tagged, and returned to the pond. After a few days, 50 fish were caught again, 2 of which were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, the approximate number of fish in the pond is ____.

Question

In a certain pond, 50 fish were caught, tagged, and returned to the pond. After a few days, 50 fish were caught again, 2 of which were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, the approximate number of fish in the pond is ____.

Accepted Answer

Concept- The approximate number of fish in the pond is 1250.
To solve this question, first we will have to find the percentage of tagged fish in the second catch.
Then, we will assume the total number of fishes in the pond to be

.
Now, as per the data provided in the question, we will use this formula to form a linear equation of single variable

which is,

Solving for

will give us our desired answer.
50 fish were caught, tagged, and returned to the pond in the first catch.
In the second catch, 50 fish were caught again, 2 of which were found to have been tagged.
And, percent of tagged fish in the second catch approximates the percent of tagged fish in the pond.
Therefore, the total number of tagged fishes in the pond = 50.
Since, in the second catch, 2 of 50 fishes we were found tagged, therefore,
percent of tagged fish in the pond

.
And, already assumed, total number of fish in the pond =

. Then,

Hence, the correct answer is 1250.

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