Each of these questions consists of a question followed by informations in three statements. You have to study the question and the statements and decide that information in which of the statement(s) is/are necessary to answer the question.
At what time will the train reach City A from city B?
(A) The train crosses another train of length of 200 meters and running in opposite direction in 15 sec
(B) The train leaves city B at 18.15 pm for city A, situated at a distance of 560 kms.
(C) The 300 m long train crosses a signal pole in 10 secs

Options

A. A) Only A
B. B) Only B
C. C) Only C
D. D) Only B and C

Answer

To solve the question "At what time will the train reach City A from City B?", we need to analyze the three statements provided and determine which of them are necessary to find the answer.

### Step-by-step Solution:

1. **Understanding the Question**:
- We need to find the arrival time of the train at City A, starting from City B.

2. **Analyzing Statement (A)**:
- Statement (A) states that the train crosses another train of length 200 meters running in the opposite direction in 15 seconds.
- This information is about the interaction between two trains but does not provide any direct information about the speed of our train or the time it takes to reach City A. Thus, this statement is **not necessary**.

3. **Analyzing Statement (B)**:
- Statement (B) states that the train leaves City B at 18:15 PM for City A, which is situated at a distance of 560 km.
- This statement provides the departure time and the distance to be traveled. This is crucial for calculating the arrival time. Thus, this statement is **necessary**.

4. **Analyzing Statement (C)**:
- Statement (C) states that a 300-meter-long train crosses a signal pole in 10 seconds.
- This statement allows us to calculate the speed of the train. Speed can be calculated using the formula: Speed = Distance / Time. Here, the distance is 300 meters and the time is 10 seconds.
- The speed of the train is 300 meters / 10 seconds = 30 meters/second, which can be converted to km/h (30 m/s * 18/5 = 108 km/h). This speed is necessary to calculate the travel time for the distance of 560 km. Thus, this statement is **necessary**.

5. **Calculating the Arrival Time**:
- From Statement (B), the train leaves at 18:15 PM.
- From Statement (C), we calculated the speed of the train as 108 km/h.
- To find the time taken to travel 560 km at a speed of 108 km/h, we use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{560 \text{ km}}{108 \text{ km/h}} \approx 5.185 \text{ hours} \]
- Converting 0.185 hours into minutes:
\[ 0.185 \times 60 \approx 11.1 \text{ minutes} \]
- Therefore, the total travel time is approximately 5 hours and 11 minutes.

6. **Calculating the Arrival Time**:
- Adding 5 hours and 11 minutes to the departure time (18:15):
- 18:15 + 5 hours = 23:15
- 23:15 + 11 minutes = 23:26
- Therefore, the train will reach City A at approximately **23:26 PM**.

### Conclusion:
- The necessary statements to answer the question are **(B)** and **(C)**.
- The train will reach City A at **23:26 PM**.