a) 12 minutes
b) 24 minutes
c) 30 minutes
d) 36 minutes

Answer: b
Explanation:

A . . . . . (+) 30 minutes
B . . . . . (+) 45 minutes
C . . . . . (-) 36 minutes
⇒ Water filled by (A + B) in 12 min
= 12 × (6 + 4)
= 12 × 10 = 120 liters
⇒ Remaining capacity
= 180 – 120 = 60 liters
⇒ After 12 minutes emptied pipe C is also opened
⇒ Total capacity (A + B – C)
= (6 + 4 – 5) = 5 liters/minutes
⇒ Time taken by (A + B – C) with capacity 5 liters/minutes to fill the remaining part
$$ = \frac{{60\,\,{\text{liters}}}}{{5\,\,{\text{liters/minutes}}}}{\text{ = 12 minutes}}$$
⇒ Therefore, total time in which the tank will be filled up is
= 12 + 12
= 24 minutes