As the pipes are operating alternatively, thus their 2 minutes job is = $\frac{1}{4}+\frac{1}{6}=\frac{5}{12}$

In the next 2 minutes the pipes can fill another $\frac{5}{12}$ part of cistern.

Therefore, In 4 minutes the two pipes which are operating alternatively will fill $\frac{5}{12}+\frac{5}{12}=\frac{5}{6}$Remaining part = $1-\frac{5}{6}=\frac{1}{6}$

Pipe A can fill $\frac{1}{4}$ of the cistern in 1 minute

Pipe A can fill $\frac{1}{6}$ of the cistern in = $\frac{2}{3}$ min

Therefore, Total time taken to fill the Cistern

**4 + $\frac{2}{3}$ minutes.**

Exam Prep: CAT , Bank Exams , AIEEE

Job Role: Bank PO , Bank Clerk