Question

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?

Answer 1

Correct Question :- In a booklet, containing 20 pages , 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 ?

(a) 5,6

(b) 7,8

(c) 9, 10

(d) 11, 12

Solution :-

Let us assume that, the numbers written on the both sides of the missing page are x and (x + 1).

So,

→ Actual sum of all 20 pages = 195 + x + (x + 1) = (196 + 2x)

Now, we know that,

• sum of first n natural numbers = n(n + 1)/2 .

So,

→ Total sum of the page numbers, containing 20 pages = (20*21)/2 = 10 * 21 = 210.

Therefore,

→ 196 + 2x = 210

→ 2x = 210 - 196

→ 2x = 14

dividing both sides by 2,

→ x = 7 .

Than,

→ x + 1 = 7 + 1 = 8 .

Hence, The torn page contains (7 and 8) Number. (Option B).

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