Institution: Bangladesh Bank Exam: অফিসার (ক্যাশ ) - Sonali | Rupali | BD Krishi | Rajshahi Krishi Unnayn | Investment Corporation Of Bangladesh - ২৯. ০৩.২০১৯ ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To find the time it takes for two trains of equal length running in opposite directions to cross each other, we need to first determine their speeds and then use these to calculate the time of crossing.

Let the length of each train be \( L \). The speed of the first train is calculated as follows: it passes a pole in 18 seconds, so its speed \( S_1 \) is \( \frac{L}{18} \). For the second train, which passes the pole in 12 seconds, its speed \( S_2 \) is \( \frac{L}{12} \).

When they cross each other, they need to cover a total distance equal to the sum of their lengths, which is \( L + L = 2L \). The combined speed when moving in opposite directions is \( S_1 + S_2 \):

\[
S_1 + S_2 = \frac{L}{18} + \frac{L}{12}
\]

To combine these fractions, we find a common denominator, which is 36:

\[
S_1 + S_2 = \frac{2L}{36} + \frac{3L}{36} = \frac{5L}{36}
\]

Now, the time \( T \) taken to cross each other can be calculated using the formula:

\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{2L}{\frac{5L}{36}} = \frac{2L \times 36}{5L} = \frac{72}{5} = 14.4 \text{ seconds}
\]

Thus, the two trains will cross each other in **14.4 seconds**, confirming that the correct choice is **D) 14.4 seconds**.