In $1$ minute, $\frac{3}{7}$ of a bucket is filled. The rest of the bucket can be filled in

### Concept & Unitary Method The problem can be solved using the unitary method. If a certain fraction of work is completed in a given time, we can find the time taken for the remaining fraction by first calculating the time for the whole work, or by setting up a direct proportion. ### Step-by-Step Solution * **Given:** Part of the bucket filled in $1$ minute = $\frac{3}{7}$. * **Calculate remaining part:** The whole bucket is $1$. The remaining part to be filled is $1 - \frac{3}{7} = \frac{4}{7}$. * **Set up proportion:** Time taken to fill $\frac{3}{7}$ of the bucket = $1$ minute. Time taken to fill $1$ (whole) bucket = $1 \times \frac{7}{3} = \frac{7}{3}$ minutes. * **Find time for remaining part:** Time taken to fill $\frac{4}{7}$ of the bucket = (Time for whole bucket) $\times$ (Remaining part) $= \frac{7}{3} \times \frac{4}{7} = \frac{4}{3}$ minutes. ### Exam Strategy & Shortcut Use direct ratios. The parts are $3$ and $4$ (since $3/7$ is filled, $4/7$ remains). If $3$ parts take $1$ minute, then $1$ part takes $\frac{1}{3}$ minute. Therefore, $4$ parts will take $4 \times \frac{1}{3} = \frac{4}{3}$ minutes. ### Common Pitfall A common mistake is finding the time to fill the *entire* bucket ($\frac{7}{3}$ minutes) and mistakenly selecting that as the answer, forgetting the question asks for the time to fill the *rest* of the bucket. ### Final Answer Therefore, the correct answer is **$\frac{4}{3}$ minutes**.