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One page is torn from a book whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages in 195. The torn page contains which of the following numbers?

One page is torn from a book whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages in 195. The torn page contains which of the following numbers? Correct Answer 7, 8

Given:

One page is torn from a book whose papers are numbered in the usual manner starting from the first page as 1

Sum of the numbers on the remaining pages = 195

Formula used:

Sum of first n natural numbers = (n/2)(n+1)

Calculation:

According to question, the sum is 195

The sum of number of torn pages in book be x

so, total sum will be 195 + x

So,

⇒ 195 + x = (n/2)(n+1)  (number of page start from 1 which is a natural number)

Now see some value near to make sum equal to 195 for this

At n = 19, sum of pages will be 190 so this cannot be considered

Now at 20, sum of pages = 210 

So the number of pages must be 20

Now we can assume that

⇒ 195 + x = 210

⇒ x = 15

∴ The torn page contains 7 and 8 numbers in it and total will be 15. 

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