For a given reaction of the first order, it takes 15 minutes for the concentration to drop from 0.8 M to 0.4 M. The time required for the concentration to drop from 0.1 M to 0.025 M will be:
k=0.69315=0.0462 min−1
Now the time taken for the concentration to drop from 0.1 M to 0.025 M
t=2.303klog0.10.025=2.3030.0462log0.10.025≈30min
Hence, option (c) is correct.