P1 can fill the tank in 8 hours while P2 can fill the tank in 12 hours therefore when Both the pumps are opened simultaneously they can fill
+= this much of tank in an hour.Therefore Time required by P1 and P2 to fill full tank is 24 Hence they can fill half the tank in
=2.4 hours. After all the 3 pipes are opened the tank will be filled at the rate of
+−= therefore for filling the remaining tank we will need 6 more hours. If supervisor was planning to come exactly when the tank is fully filled then he must come after 8.4 hours
Time required by P1 and P2 to fill 1/3rd of the tank is
==1.6 hours therefore supervisor will come after
=8.4−1.6=6.8 hours
In 6.8 hours all the three pipe will fill
=0.56 of the capacity of tank
therefore remaining tank to be filled when the supervisor comes
=1−0.56−0.33≈0.1 i.e. 10%
Therefore option 'C' is our answer