Question

The sum of page numbers of a book came out to be 1288. However, one page number was counted twice. Find which page number was counted twice.​

Answer 1

Answer:

ANSWER

Let page numbers of open pages be x andx+1

Then according to the question,

x+x+1=373

2x=372

x=186

The pages are 186 and 187.

Answer 2

Answer:

The page number that counted twice = 13    

Step-by-step explanation:  

Given data

The sum of the page numbers of a book = 1288

and one page number was counted twice

Here we need to find which number is counted twice

let n be the number of pages in the book

and we know page numbers will be 1 , 2, 3..

then sum of page numbers will be

⇒ ( 1 + 2 + 3 ...up to n (natural numbers) = 1288 _(1)

⇒ we know that sum of n natural numbers = $\frac{n(n+1)}{2}$_ (2)

⇒ from (1) and (2) ⇒  $\frac{n(n+1)}{2} = 1288$

                             ⇒ n (n+1) = 2576 [ it will not satisfy for any number as one number is counted twice]

⇒ the most appropriate value for "n" which can give nearest value to 2576  is  50

⇒ 50(50+1) = 2550      

⇒ subtract 2550 from 2576 ⇒ 2576 - 2550 = 26 = 2(13)

⇒ the page number that was counted twice = 13