Indian Institute of Foreign Trade 2009 Solved Paper

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 $\frac{1}{8}+\frac{1}{12}=\frac{5}{24}$ 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 $\frac{12}{5}=2.4$ hours. After all the 3 pipes are opened the tank will be filled at the rate of $\frac{1}{8}+\frac{1}{12}-\frac{1}{8}=\frac{1}{12}$ 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 hoursTime required by P1 and P2 to fill 1/3rd of the tank is $\frac{24}{5\times 3}=\frac{8}{5}=1.6$ hours therefore supervisor will come after $=8.4-1.6=6.8$ hoursIn 6.8 hours all the three pipe will fill $\frac{6.8}{12}=0.56$ of the capacity of tanktherefore remaining tank to be filled when the supervisor comes $=1-0.56-0.33\approx0.1$ i.e. 10%Therefore option 'C' is our answer