How many fish were originally caught by Mr X in total?

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SUMMARY

Mr. X originally caught 6825 fish based on a mathematical puzzle involving modular arithmetic. The problem states that when the fish are arranged in rows of 9, 3 remain; in rows of 10, 2 remain; and in rows of 11, none remain. The solution involves setting up the equations 9n + 3 = 110m + 5, where m is a natural number. By analyzing the constraints and assuming a 3% error, the correct total of fish is determined to be 6825.

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bhavinsinh
numbers puzzle...

Mr X catches 7000 fish appox from a sea.When he lines up the fish in rows of 9 three remain.
These three fish are thrown.He then lines up the remaining fish in rows of 10.THis time two fish remain and again they are thrown in the sea.Finally he lines up the remaining fish in rows of 11 and no fish remain .How many fish were there in the beginning...I know its a common puzzle but I am not able to come up with a solution.a mathematical solution would be appreciated..
 
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Outline of the solution:
The number of fish x = 9n+3 = 110m+5 for natural numbers m, n. Assuming error of 3%, m is between 62 and 65. Hence, there are 6825 fish since 9 divides 110 m + 2 at m = 62.
 
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