Pipe A can fill an empty cistern in 6 hours and pipe B can fill the same empty cistern in 8 hours. Both the pipes are opened simultaneously but after two hours, pipe A is closed. How many hours will B take to fill the remaining part of the cistern?

Let's assume the total capacity of the cistern is 24 units.

Pipe A can fill an empty cistern in 6 hours and pipe B can fill the same empty cistern in 8 hours.

Efficiency of Pipe A = $$\frac{24}{6}$$ =  4 units/hour

Efficiency of Pipe B = $$\frac{24}{8}$$ = 3 units/hour

Both the pipes are opened simultaneously but after two hours, pipe A is closed. Let's assume B will take 'y' hours to fill the remaining part of the cistern.

2(Efficiency of Pipe A+Efficiency of Pipe B) + y(Efficiency of Pipe B) = 24

$$2\times(4+3) + y\times3 = 24$$

$$2\times7 + 3y = 24$$

$$14 + 3y = 24$$

$$3y = 24-14$$

$$3y = 10$$

y = $$\frac{10}{3}$$

= $$3\frac{1}{3}$$ hours