Let the slower pipe fill the tank in x minutes, then the faster pipe will fill the tank in (x/5) minutes.

According to the given condition, the faster pipe takes 48 minutes less than the slower pipe to fill the tank. So, we have:

x - (x/5) = 48

Simplifying the above equation, we get:

4x/5 = 48

x = 60

Therefore, the slower pipe will fill the tank in 60 minutes and the faster pipe will fill the tank in 12 minutes (x/5 = 60/5 = 12).

Now, to find the time taken by both pipes together to fill the tank, we use the following formula:

Time taken by both pipes together = (Time taken by slower pipe × Time taken by faster pipe) / (Time taken by slower pipe + Time taken by faster pipe)

Substituting the values, we get:

Time taken by both pipes together = (60 × 12) / (60 + 12)

= 720/72

= 10

Therefore, both pipes together will fill the tank in 10 minutes.

Hence, the correct answer is option D, 10 min.

Let's understand the concepts and formulas used in this problem in more detail:

• Pipes and Cisterns: In the pipes and cisterns problems, we deal with the time taken by pipes or cisterns to fill or empty a tank. We use the formula:

Work done = (Rate of work × Time taken)

• Rate of work: Rate of work is the amount of work done by a pipe or cistern in one unit of time. We use the formula:

Rate of work = 1 / Time taken

• Time and Work: In the time and work problems, we deal with the time taken by a person or machine to complete a task. We use the formula:

Work done = (Efficiency × Time taken)

• Efficiency: Efficiency is the amount of work done by a person or machine in one unit of time. We use the formula:

Efficiency = Work done / Time taken

By using the above concepts and formulas, we have solved the given problem to find the time taken by both pipes together to fill the tank, which is 10 minutes.