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

We know that the sum of n consecutive natural numbers = n(n+1)/2.

Natural numbers are integers starting with 1.

Now according the information given in question our value of n(n+1)/2 should be greater than 195.

Why? Because one page is torn, so the sum is less than what it should be. Right?

If we take n = 19 we will get n(n+1)/2 = 19 × 20/2 = 190 which is less than 195.

So taking next number let’s assume n = 20.

In this case – n(n+1)/2 = 20×21/2 = 210. But two consecutive numbers were removed, so 210 – 195 = 15. It means that the sum of the two consecutive torn pages should be 15. Only option (b) matches.