Question

in a 25 pages book a paper sheet which is having page no.on both sides missed.the sum of the remaining page numbers is 302.then find out missing page numbers on the papersheet?

Answer 1

Number on pages forms following A.P

1 , 2 , 3 , 4 , 5 , 6 ........................... 25

first term = a1 = 1

common difference = d = 1

Sum of series = Sn = (n/2)( a + l )  

where n is number of terms ,  a= first term and l is last term

in our case n = 25 , a = 1 and l = 25

⇒Sn = (25/2)( 1 + 25 ) = 25 × 13 = 325

so summation of number from 1 to 25 = 325

given sum of remaining pages = 302

so sum of two consecutive numbers  on missing page =  325 - 302 = 23

let one number be x , so other number will be x + 1

and x + ( x+1) = 23

⇒2x = 22

⇒ x = 11 and x +1 = 12

hence two missing numbers on both side of a page are 11 and 12.