An empty tank be filled with an inlet pipe ‘A’ in 42 minutes. After 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled. Find the time taken to fill the tank?	Choose the correct choice from the following answers.
A) 51.6  B) 51.5  C) 51.7  D) 51.1  E) 51.0

Rationale: assume total tank capacity = 210 liters now capacity of pipe a = 210 / 42 = 5 liters capacity of b = 210 / 30 = - 7 liters capacity of c = 210 / 35 = 6 min assume tank gets filled in x min after the third pipe got opened . so x × 5 + 6 × ( − 2 ) + 4 x = 210 x × 5 + 6 × ( − 2 ) + 4 x = 210 ⇒ 48 + 4 x = 210 ⇒ 4 x = 162 ⇒ x = 40.5 ⇒ 48 + 4 x = 210 ⇒ 4 x = 162 ⇒ x = 40.5 total time taken to fill the tank = 40.5 + 12 + 6 = 51.5 answer : b
Answer: B