Question

In a certain pond, 50 fish were caught, ragged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 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, what is the approximate number of fish in the pond?

Answer 1

Hint: To solve this question, first, we will find the percentage of fish in the second catch which was from the first catch. And then what we will do is we will put the percentage of fish in second catch equals to the percentage of 50 fishes out of total fish in the pond, to get the total number of fishes.

Complete step-by-step solution:
Now, in question, it is given that firstly 50 fish were caught, tagged, and were returned to the pond.
So, the number of fish caught = 50.
Now, also it is given that after few days again 50 fish were caught and out of which 2 were tagged fish.
That is when 50 fishes were caught in the first attempt which was tagged out of 50, 2 were found in the second time of catching.
So, the percentage of tagged fish in second catch will be equals to,
$=\dfrac{2}{50}\times 100%$
\[=2\times 2%\]
$=4%$
So the percentage of tagged fish in the second catch is equaled to 4 %.
Now, it is said in question that the percentage of tagged fish in the second catch approximates the percentage of tagged fish in the pond which means if there are total x fish in the pond then the percentage of 50 out x is equivalent to the percentage of tagged fish in second catch which is 4%.
So, if there are total x fish in the pond the, according to the above statement we can rewrite the above situation in form of the equation as,
$\dfrac{50}{x}\times 100\%= 4\%$
On simplifying we get,
\[\dfrac{50}{x}=\dfrac{2}{50}\]
Taking x from the denominator on the left-hand side to the numerator on the right-hand side, 50 from the denominator on the right-hand side to the numerator on the left-hand side, and 2 from the numerator on right-hand side to the denominator on the left-hand side, using cross multiplication, we get
\[x=50\times \dfrac{50}{2}\]
On solving we get,
\[x=1250\]
Hence, the number of fish in ponds is equals to 1250.

Note: While solving percentage problems, one must know the formula of finding the percentage. Read questions twice to understand what exactly the question means. Always remember that if we have to calculate the percentage of x objects from total y objects, then the percentage will be $\dfrac{x}{y}\times 100\%$. Calculation error must be avoided while you do cross-multiplication as it will change the answer and hence solution will get incorrect.