A pipe normally takes 4 min to fill a bucket. Due to a hole in the bucket, it takes 6 min. In how much time will the hole empty the full bucket?

Correct option is C

​$$\text{Let the total capacity of the bucket be } 1 \text{ unit.}$$

$$\text{The pipe can fill the bucket in } 4 \text{ minutes, so its filling rate is:}$$ $$\frac{1}{4} \text{ of the bucket per minute}$$

$$\text{Due to the hole, the bucket is filled in } 6 \text{ minutes, meaning the net filling rate is:}$$​$$\frac{1}{6} \text{ of the bucket per minute}$$

$$\text{The hole is leaking water, reducing the net filling rate. So, the leakage rate of the hole is:}$$​$$\text{Leakage rate} = \text{Filling rate} - \text{Net filling rate}$$

$$\frac{1}{4} - \frac{1}{6} = \frac{3}{12} - \frac{2}{12} = \frac{1}{12} \text{ of the bucket per minute}$$

$$\text{Thus, the hole alone will take } 12 \text{ minutes to empty the full bucket.}$$

$$\therefore \mathbf{12 \text{ min}}$$​​​​​​​

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