And I came up with an out of box answer:
Since most of the work is in going down and climbing up floors again. Thus at a given floor one can drop one egg down, and throw the second one up in the air, thus since you can throw an egg up around 2-3 floors at least. The egg will attain a certain height which you can approximate visually and then check if the egg breaks or not after falling down. This will significantly reduce number of floors that you would need to climb.
and I got called for next round of interviews!
