Two pipes A and B can fill an empty cistern in 4.8 and 7.2 hours, respectively. Pipe C can drain the entire cistern in 9.6 hours when no other pipe is in operation. Initially when the cistern was empty, Pipe A and Pipe C were turned on. After a few hours. Pipe A was turned off and Pipe B was turned on instantly. In all it took 16.8 hours to fill the cistern. For how many hours was Pipe B turned on?

Two pipes A and B can fill an empty cistern in 4.8 and 7.2 hours, respectively. Pipe C can drain the entire cistern in 9.6 hours when no other pipe is in operation. Initially when the cistern was empty, Pipe A and Pipe C were turned on. After a few hours. Pipe A was turned off and Pipe B was turned on instantly. In all it took 16.8 hours to fill the cistern.

Time Taken      Work Done           Efficiency

A - 4.8      LCM (4.8,7.2,9.6)    $$\frac{28.8}{4.8} =6$$

B - 7.2                = 28.8                  $$\frac{28.8}{7.2}=4$$

C - 9                                                $$\frac{28.8}{9.6} =3$$

Let x be time for which Pipe A was open

So according to question,

$$(A-C)\times x +(B-C)(16.8-x) =28.8$$

$$(6-3)\times x +(4-3)(16.8-x) =28.8$$

$$2x+16.8 =28.8$$

$$2x =12$$

$$x =6$$

So B is open for$$ (16.8-6) = 10.8$$

Option D is correct.