In the given questions two quantities are given one as quantity I and another as quantity II you have to determine relationship between two quantities choose appropriate option
Trains A,B travelling at speed of 72kmph and 90kmph respectively in same direction cross each other in 4 min 21 sec. Train A crosses 360 metres long platform in 54 seconds running at the same speed.
quntityI:length of train B
quantityII:length of train A

Options

A. `IltII`
B. `IgtII`
C. `IleII`
D. `IgeII`

Answer

To solve the problem, we need to find the lengths of Train A and Train B based on the information provided. Let's break it down step by step.

### Step 1: Convert Speeds from km/h to m/s
- Train A's speed = 72 km/h
- Train B's speed = 90 km/h

To convert km/h to m/s, we use the formula:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]

Calculating for Train A:
\[ 72 \times \frac{5}{18} = 20 \text{ m/s} \]

Calculating for Train B:
\[ 90 \times \frac{5}{18} = 25 \text{ m/s} \]

### Step 2: Calculate the Time Taken to Cross Each Other
The time taken for the trains to cross each other is given as 4 minutes and 21 seconds. We need to convert this to seconds:
\[ 4 \text{ minutes} = 4 \times 60 = 240 \text{ seconds} \]
Adding the additional 21 seconds:
\[ 240 + 21 = 261 \text{ seconds} \]

### Step 3: Set Up the Equation for Crossing Each Other
When two trains cross each other, the distance covered is the sum of their lengths. The relative speed when they are moving in the same direction is the difference of their speeds:
\[ \text{Relative Speed} = 25 \text{ m/s} - 20 \text{ m/s} = 5 \text{ m/s} \]

Using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
The combined length of Train A and Train B is:
\[ L_A + L_B = 5 \text{ m/s} \times 261 \text{ seconds} = 1305 \text{ meters} \]

### Step 4: Calculate Length of Train A
Train A crosses a 360-meter long platform in 54 seconds. The distance covered is the length of Train A plus the length of the platform:
\[ L_A + 360 = \text{Speed of Train A} \times \text{Time} \]
Substituting the known values:
\[ L_A + 360 = 20 \text{ m/s} \times 54 \text{ seconds} \]
Calculating the right side:
\[ L_A + 360 = 1080 \text{ meters} \]
Now, solving for \(L_A\):
\[ L_A = 1080 - 360 = 720 \text{ meters} \]

### Step 5: Calculate Length of Train B
Now we can find the length of Train B using the equation from Step 3:
\[ L_A + L_B = 1305 \text{ meters} \]
Substituting \(L_A\):
\[ 720 + L_B = 1305 \]
Solving for \(L_B\):
\[ L_B = 1305 - 720 = 585 \text{ meters} \]

### Conclusion
- Length of Train A (\(L_A\)) = 720 meters
- Length of Train B (\(L_B\)) = 585 meters

### Comparison of Quantities
- Quantity I: Length of Train B = 585 meters
- Quantity II: Length of Train A = 720 meters

Thus, we conclude that:
\[ \text{Quantity I} < \text{Quantity II} \]

### Final Answer
The answer is that Quantity I is less than Quantity II.

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