Pipes A, B and C can fill a tank in 10, 15 and 30 hours, respectively. D is an emptying pipe which alone can empty the full tank in x hours. A, B and C are opened together for 3 hours and then closed. Now D is opened which alone empties the tank in 30 hours. What is the value of x ?

 Let the  D is empty the tank = $$x $$hours 

Pipe A, B, and C can fill the tank = 10 hours, 15 hours, and 30 hours 

take Lcm A, B, C, and D  = 30

so A efficiency = 3$$x$$ ,B efficiency = 2$$x $$ , C efficiency = $$x$$ and D efficiency = 30

we know that capcity = $$  efficiency \times time$$

 According to the question  (A+B+C) together work to 3 hours 

then capcity of tank fill in 3 hours =$$ (A+B+C)\times 3 = 6x \times 3 = 18x $$

Now D alone can empty 18$$x$$ in 30 hours

so  $$ 18x = D   efficiency \times 30 $$

$$\Rightarrow 18x = 30 \times 30 $$ (put the value)

$$\Rightarrow x = \dfrac{30\times 30}{18}$$

$$\Rightarrow x = \dfrac{900}{18}$$

$$\Rightarrow x = 50$$ hours Ans