If 4/9 th of a bucket is filled in 1 minute, the rest of it will be filled in ?

Answer: Option C

Remaining part
$$\begin{array}{rl}& =\left(1-\frac{4}{9}\right)\\ & =\frac{5}{9}\end{array}$$
Let the required time be x minutes
More volume to be filled , More time taken (Direct proportion)
$$\begin{array}{rl}& \therefore \frac{4}{9}:\frac{5}{9}::1:x\\ & \Rightarrow \frac{4}{9}x=\frac{5}{9}\\ & \Rightarrow x=\left(\frac{5}{9}\times \frac{9}{4}\right)\\ & \Rightarrow x=\frac{5}{4}\end{array}$$