The correct option is C 2.5 g
The half-life t12, by definition, is the period of time after which the sample size (number ) becomes half. For 60Co, since t12=270 days, after 270 days, there will be only half the nuclei left after the β decay, and the sample will weigh only 5 g, since you started off with 10 g. So now your sample weighs 5 g, and contains that many nuclei.
After another period of 270 days, half of that will remain, i.e. only 2.5 g. Therefore, after two half-lives, or 540 days, the sample will weigh only 2.5g.
Generally, if you have N0 nuclei in the sample at present, only N02n will remain after n half-life periods, or at t=n×t12,N=N02nThink about it.