A number theory problem by Yash Khatri
Number Theory
Level
3
When the zoo authorities increased the entry fee by 25% last year, the number of visitors coming to the zoo went down drastically and the overall ticket revenue came down by 25%. By what percentage did the number of visitors go down? (Don't put the % symbol)
The answer is 40.
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Let the original ticket price be 'p' and the original number of visitors be 'n'. Initial revenue = n x p.
Now, this has gone down by 25%. Therefore, new revenue = (1 - 0.25)np = 0.75 np.
Let the new number of visitors be N. Since the ticket price is increased by 25%. new ticket price P = 1.25p. New revenue = 1.25Np.
Equating both, we get 1.25Np = 0.75np. This means, N = (0.75/1.25)n = 0.6n.
Therefore, the number of visitors has gone down by 0.4n = 40%.