All the fractions are based on 80 patients: 1/8 is 80/8=10; 1/4 is 80/4=20; 1/5 is 80/5=16 so 2/5 is 32. In all, 10+20+32=62 patients were discharged. That leaves 80-62=18. 30 new patients were admitted: 18+30=48 in the ward. So the number of empty beds is 80-48=32.