Q. 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?

Explanation : 

Torn pages numbers from a booklet ??

Let’s solve this step by step.

1) In a booklet, pages are numbered consecutively starting from 1.
2) When one page (which has numbers on both sides) is torn out, the sum of remaining numbers is 195.
3) Let’s say the last page number in the booklet is n.

4) Sum of all numbers from 1 to n = n(n+1)/2

5) When one page is torn out, it removes two consecutive numbers (front and back). Let’s call these numbers x and x+1.

6) So: [n(n+1)/2] – (x + (x+1)) = 195
Or: [n(n+1)/2] – (2x + 1) = 195

7) Let’s try some values:
If n = 20:
20×21/2 = 210
210 – (2x + 1) = 195
210 – 195 = 2x + 1
15 = 2x + 1
14 = 2x
x = 7

8) When x = 7, the torn page would have numbers 7 and 8.

9) Let’s verify:
– Total sum for n=20 is 210
– Removing 7 and 8 gives 210 – 15 = 195 ✓

Therefore, the torn page contains the numbers 7 and 8.

The answer is (b) 7, 8