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The number of persons who booked ticket for the New Year’s concert is a perfect square. If 100 more persons booked ticket then the number of spectators would be a perfect square plus 1. If still 100 more persons booked ticket then the number of spectators would be again a perfect square. How many persons booked ticket for the concert?

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15 comments

      1. Sir, I meant the square root of the number of people who attended the concert will be greater than 40. This is because no squares of natural numbers below 40 fit the pattern as mentioned in the question 🙂

    1. Abhishek Tandon

      My approach:
      a^2+100=b^2+1
      b^2-a^2=99

      b^2+101=c^2
      c^2-b^2=101
      (c-b)(c+b)=101
      Since 101 is prime
      So, factors must be prime and 1
      c-b=1 means c=b+1
      c+b=101 means 1+2b=101
      b= 50
      c=51
      Hence a=49

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