The filling efficiency of pipe A is 4 times faster than second pipe B. If B takes 30 minutes to fill a tank, then determine the time taken by them to fill a tank together.

Let the efficiency of pipe \(B\) be \(x\). Then the efficiency of pipe \(A\) is \(5x\) since it is 4 times faster than pipe \(B\).

Since pipe \(B\) takes 30 minutes to fill the tank, its filling rate is \(\frac{1}{30}\) of the tank per minute.

Therefore, we can say:
\[x = \frac{1}{30}\]

Now, let’s find the combined filling rate of both pipes when they work together. The combined rate is the sum of the individual rates of pipes \(A\) and \(B\):

\[\text{Combined rate} = \text{Rate of A} + \text{Rate of B} = 5x + x = 6x\]

Substituting the value of \(x\):
\[6x = 6 \times \frac{1}{30} = \frac{1}{5}\]

This means that when both pipes \(A\) and \(B\) work together, they fill \(\frac{1}{5}\) of the tank per minute.

To find the time taken to fill the tank together, we can take the reciprocal of the combined rate:
\[\text{Time taken} = \frac{1}{\text{Combined rate}} = \frac{1}{\frac{1}{5}} = 5 \text{ minutes}\]

So, it takes 5 minutes for both pipes \(A\) and \(B\) to fill the tank together.