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 ?

50

A+ = 10 hrs, B+ = 15 hrs, C+ = 30 hrs,

⇒ A + B + C opened for 3 hours = (3 + 2 + 1) x 3 = 6 x 3 = 18 units,

⇒ D takes x hrs to completely empty the tank, and take 30 hours to empty 18 units of tank = \(\frac{18}{30}\) = \(\frac{3}{5}\) ..(Efficiency of D)

⇒ Therefore, value of x is = \(\frac{3}{5}\) x X = 30,

⇒ x = 50 hrs.