Numbers from 1 to 100 are written on the blackboard. The teacher
calls students and instructs to strike out any two numbers and replace
them with their sum. This goes on till only one number remains.
What is that number?

(a) 5000
(b) 5050 (ans)
(c) Depends on the sequence of erasing numbers

Please explain how?

if one strikes out two numbers and then writes the sum , eventually all the numbers get striked out and is replaced by the sum

so the answer is nothing but the sum of numbers from 1 - 100

so answer is

1+2+3+4+5+6......+97+98+99+100

the sum of this sequence has the formula n*(n+1) / 2

so n = 100 here

n+1 = 101

so calculating n*(n+1)/2 we get 100*101 / 2

= 10100/2 = 5050 !

approve if the answer is correct !

See if U go an cancelling Two Two numbers and go on replacing them by their sum, the numbers are replaced by single numbers and the numbers go on decreasing.......... BEST way to explain this is by taking an example :-

Consider numbers from 1,2,3,............10

1.Strike any two nos such as 3 & 9 (They r my favrate), replace by 12

2.Strike any two nos such as 5 & 8, replace by 13

3.Strike any two nos such as 12 & 13, replace by 25

4.Strike any two nos such as 1 & 2, replace by 3

5.Strike any two nos such as 25 & 3, replace by 28

6.Strike any two nos such as 28 & 4, replace by 32

7.Strike any two nos such as 32 & 10, replace by 42

8.Strike any two nos such as 6 & 7, replace by 13

9. Now on two numbers remain they are 42 & 13, replace them by 55

Thus a single no. remains which is the sum of all nos from 1 to 10 and another fact is the no of transactions required for this are n-1 = 10-1 = 9

Thus from 1 to 100, sum is 5050 and thus the ans is option b

The sum of first n numbers is given by n(n+1)/2

so we have to find sum of first 100 no 

by formula 100*101/2

=50*101

=5050

So last digit is 5050

HENCE B IS CORRECT