What is your reaction if the administration asked you to perform extra work to a colleague resigned/ careless in his work?

There is no right or wrong answer to this question. If your colleague is careless, the issue is to taken by the management separately.

 However, when you are asked to do the job, you should welcome this (unless you have serious emergency) and certainly you can claim overtime (if rules permit) or request administration for day-off in lieu of overtime (if rules permit).  It is noted here this stop gap measure shall not be continued for long and administration has to find a suitable solution

I'm going to work

That I can,

Wholeheartedly

Thanks

No doubt i will do it , but as colleague Rami mentioned for once or twice .not for a long time

Simply do it soon and go back to home.  nothing to say or react if he is very intelligent and he knows about the present situation to get another job from a very tight and competitive job market.

I agree with Mr. Fazlur Rahman answer and have voted for him

Answered well by experts here

I would refuse if it will be on a long time basis but if it is a one time task and then back to normal it is ok.

we can accept it but if that do for ever no we didn't accept

I agree with the rest of the answers

First that person should be replaced if he/she showed constant reluctance. And I wouldn't mind performing his/her task until a solution is found for that matter. 

We as human being resist to change and the same will be my reaction. I would have to analyse my current situation with work, I am generally overloaded with my current profile and hence I would not like to take up this new assignment. I would try to make management aware of possibility that I might not be very efficient with two profiles (extra work).

If it is forced on me than there will be no choice but to accept management decision.