Institution: Bangladesh Bank Exam: Officer (Cash) -Sonali Bank | BD Development | BD Krishi Bank - 12.10.2018 ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, we need to determine the speed of the second train given the train's length and how long it takes to pass a pole and another train.

1. **Passing a Pole**: The first train is 150 m long and passes a pole in 15 seconds. We can calculate the speed of the first train using the formula:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{150 \, \text{m}}{15 \, \text{s}} = 10 \, \text{m/s}
\]

To convert this speed to km/h, we multiply by 18/5:

\[
10 \times \frac{18}{5} = 36 \, \text{km/h}
\]

2. **Crossing the Second Train**: When the two trains cross each other, they are travelling in opposite directions. As both trains are 150 m long, the total distance to be covered when they pass each other is:

\[
150 + 150 = 300 \, \text{m}
\]

Given they cross each other in 8 seconds, we can find the combined speed (sum of speeds of both trains) needed to cover this distance:

\[
\text{Combined speed} = \frac{300 \, \text{m}}{8 \, \text{s}} = 37.5 \, \text{m/s}
\]

Converting this to km/h:

\[
37.5 \times \frac{18}{5} = 135 \, \text{km/h}
\]

3. **Finding the Speed of the Second Train**: We know the first train travels at 36 km/h. If the combined speed is 135 km/h, we can find the speed of the second train:

\[
\text{Speed of second train} = \text{Combined speed} - \text{Speed of first train} = 135 - 36 = 99 \, \text{km/h}
\]

Thus, the speed of the second train is **99 km/h**, making option D the correct choice.