Explanation:

- Pipe P: Fills the tank in 44 minutes, so in 1 minute, it fills \( \frac{1}{44} \) of the tank.

- Pipe R: Fills the tank in 33 minutes, so in 1 minute, it fills \( \frac{1}{33} \) of the tank.

- Cycle Duration: Every 4-minute cycle consists of 2 minutes of Pipe P and 2 minutes of Pipe R.

- Amount Filled in 4 Minutes:

- 2 minutes of Pipe P: \( 2 \times \frac{1}{44} = \frac{1}{22} \)

- 2 minutes of Pipe R: \( 2 \times \frac{1}{33} = \frac{2}{33} \)

- Total: \( \frac{1}{22} + \frac{2}{33} = \frac{3}{66} + \frac{4}{66} = \frac{7}{66} \)

- Total Time Needed to Fill the Tank:

- After nine 4-minute cycles (36 minutes), \( 9 \times \frac{7}{66} = \frac{63}{66} \) of the tank is filled.

- Pipe P runs for another 2 minutes: \( \frac{1}{22} = \frac{3}{66} \) fills the rest.

- Total Time to Fill the Tank: 36 minutes (9 cycles) + 2 minutes = 38 minutes.

- Correct Answer: Option 2: 38 minutes