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A leaf is torn from a paperback novel.The sum of numbers on the remaining pages is 15,000.What are the page numbers on the torn leaf ?

A leaf is torn from a paperback novel.The sum of numbers on the remaining pages is 15,000.What are the page numbers on the torn leaf ?
 
 

Grade:12th Pass

1 Answers

Arun
25750 Points
6 years ago
Please find the answer to your question belowThe sum of the numbers form an arithmetic progression.So, assuming the number of pages is n, the first is number 1. And number missing are p and p+1 (a leaf is torn so two page numbers missing).Then Sum of all pages= n/2 (2+n-1) {using the formula of sum of AP with a=1}The Sum of remaining pages =15000=n/2(2+n-1)-p-(p+1);=> 15000= n+n^2/2-n/2-2p-1=> 15000=n^2/2+n/2-2p-1=>14999*2=n^2+n-4p=>4p=n^2+n-14999*2=>p=(n^2+n-14999*2)*0.25=>p=(n(n+1)-14999*2)*0.25Thus knowing the total number of pages you can determine p and p+1 numerically.

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