Let A,B and C denote the set of men who received medals in even A, event B and event C respectively.
Then, n(A)=48,n(B)=25,n(C)=18 , n(A∪B∪C)=60 and n(A∩B∩C)=5,
Now we know that, n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(A∩C)−n(B∩C)+n(A∩B∩C)
⇒60=48+25+18−n(A∩B)−n(A∩C)−n(B∩C)+5
⇒n(A∩B)+n(A∩C)+n(A∩C)=48+25+18+5−60=36
Therefore, the number of people who received medals in exactly two of the three sports will be 36−3(A∩B∩C)=36−15=21.