A printer alloted consecutive integers to all the pages of a book starting with 1 .In this process the sum of pages is $1275$ . Then the total number of pages in that book is

50

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51

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100

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101

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Solution

The correct option is A $50$
The page numbers are like $1 + 2 + 3 + 4 + 5 + 6 + \dots n$
The summ is given as $\frac{n (n + 1)}{2} = 1275 n^{2} + n = 2550 n^{2} + 51 n - 50 n - 2550 = 0 n (n + 51) - 50 (n + 51) = 0 (n - 50) (n + 51) = 0 n = 50, - 51$
Pages cannot be negitive so $n = 50$

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