To solve this problem, we need to calculate the time it will take for two trains of equal length to completely pass each other when they are moving in the same direction.

Let's denote:

• L = length of each train (in meters, since both trains are of equal length)
• S_1 = speed of the first train (in meters per second)
• S_2 = speed of the second train (in meters per second)
• Total length they need to cross = L + L = 2L

Step 1: Convert time taken to cross a pole to speed

For the first train that takes 10 seconds to cross a pole:

• Speed S_1 = \frac{L}{10}

For the second train that takes 20 seconds to cross a pole:

• Speed S_2 = \frac{L}{20}

Step 2: Calculate relative speed

Since the trains are moving in the same direction, the relative speed is the difference between their speeds:

• Relative speed = S_1 - S_2 = \frac{L}{10} - \frac{L}{20}
• Simplify the relative speed: = \frac{2L}{20} - \frac{1L}{20} = \frac{L}{20}

Step 3: Calculate time to cross each other

The time taken for these trains to cross each other completely is given by:

• Time = \frac{\text{Total length to cross}}{\text{Relative Speed}}
• Time = \frac{2L}{\frac{L}{20}} = 2L \times \frac{20}{L} = 2 \times 20 = 40 \text{ seconds}

Therefore, the trains will take 40 seconds to cross each other. Thus, the correct answer is 40 sec.

Let's briefly eliminate other options to ensure correctness:

• 10 sec and 15 sec are clearly too short for the completion of crossing, given the speeds involved.
• 30 sec is not possible as calculation based on relative speed gives precise 40 sec.