A train crosses another train in 20 sec. Find out the lengths of the trains.
A. Ratio between the lengths the of second train and first train is `4:5.`
B. Ratio between the speed of first and second trains is `1:2.`
C. The speed of first train is 36 km/hr.

Options

A. Only A and B together
B. One B and C together
C. Only A and C together
D. Can't be answerd even after using all the information

Explanation

To solve the problem, we need to analyze the information provided in the statements and determine if we can find the lengths of the trains.

### Given:
- A train crosses another train in 20 seconds.
- We need to find the lengths of the trains.

### Statements:
1. **Statement A**: The ratio between the lengths of the second train and the first train is 4:5.
2. **Statement B**: The ratio between the speed of the first and second trains is 1:2.
3. **Statement C**: The speed of the first train is 36 km/hr.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- When two trains cross each other, the distance covered (which is the sum of their lengths) can be calculated using the formula:
\[ \text{Distance} = \text{Relative Speed} \times \text{Time} \]
- Here, the time taken to cross each other is given as 20 seconds.

2. **Analyzing Statement A**:
- Let the length of the first train be \( L_1 \) and the length of the second train be \( L_2 \).
- According to Statement A, we have:
\[ \frac{L_2}{L_1} = \frac{4}{5} \implies L_2 = \frac{4}{5} L_1 \]
- This gives us a relationship between the lengths of the two trains, but we still need more information to find their actual lengths.

3. **Analyzing Statement B**:
- Let the speed of the first train be \( S_1 \) and the speed of the second train be \( S_2 \).
- According to Statement B, we have:
\[ \frac{S_1}{S_2} = \frac{1}{2} \implies S_2 = 2S_1 \]
- This gives us a relationship between the speeds of the two trains, but we still need to know the actual speeds to find the lengths.

4. **Analyzing Statement C**:
- Statement C provides the speed of the first train:
\[ S_1 = 36 \text{ km/hr} \]
- To convert this speed into meters per second (since the time is given in seconds), we use the conversion factor \( \frac{5}{18} \):
\[ S_1 = 36 \times \frac{5}{18} = 10 \text{ m/s} \]
- Now, using Statement B, we can find the speed of the second train:
\[ S_2 = 2S_1 = 2 \times 10 = 20 \text{ m/s} \]

5. **Calculating the Relative Speed**:
- Since we do not know the direction of the trains, we will assume they are moving towards each other (which gives us the maximum relative speed):
\[ \text{Relative Speed} = S_1 + S_2 = 10 + 20 = 30 \text{ m/s} \]

6. **Finding the Total Distance**:
- The total distance covered when the two trains cross each other is:
\[ \text{Distance} = \text{Relative Speed} \times \text{Time} = 30 \text{ m/s} \times 20 \text{ s} = 600 \text{ m} \]
- This distance is the sum of the lengths of both trains:
\[ L_1 + L_2 = 600 \text{ m} \]

7. **Using the Length Ratio**:
- From Statement A, we have \( L_2 = \frac{4}{5} L_1 \).
- Substituting this into the equation \( L_1 + L_2 = 600 \):
\[ L_1 + \frac{4}{5} L_1 = 600 \]
- Combining the terms:
\[ \frac{9}{5} L_1 = 600 \implies L_1 = 600 \times \frac{5}{9} = \frac{3000}{9} \approx 333.33 \text{ m} \]
- Now, substituting back to find \( L_2 \):
\[ L_2 = \frac{4}{5} L_1 = \frac{4}{5} \times \frac{3000}{9} = \frac{2400}{9} \approx 266.67 \text{ m} \]

### Conclusion:
- The lengths of the trains are approximately:
- Length of the first train \( L_1 \approx 333.33 \text{ m} \)
- Length of the second train \( L_2 \approx 266.67 \text{ m} \)