A train running at the speed of 144 km/hr crosses a man who is running at the speed of 18 km/hr in opposite direction of train in 8 sec. Find time taken by train to cross a platform, whose length is 66(2/3)% more than length of train?

Options

A. A)36 sec
B. B) 24 sec
C. C)12 sec
D. D)28 sec

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the speed of the train and the man
- The speed of the train = 144 km/hr
- The speed of the man = 18 km/hr

### Step 2: Convert the speeds from km/hr to m/s
To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \).
- Speed of the train in m/s = \( 144 \times \frac{5}{18} = 40 \) m/s
- Speed of the man in m/s = \( 18 \times \frac{5}{18} = 5 \) m/s

### Step 3: Calculate the relative speed of the train and the man
Since they are moving in opposite directions, we add their speeds.
- Relative speed = Speed of the train + Speed of the man = \( 40 + 5 = 45 \) m/s

### Step 4: Use the time taken to cross the man to find the length of the train
The train crosses the man in 8 seconds.
- Distance (length of the train) = Relative speed × Time
- Length of the train = \( 45 \times 8 = 360 \) meters

### Step 5: Calculate the length of the platform
The length of the platform is 66⅔% more than the length of the train.
- 66⅔% as a fraction = \( \frac{2}{3} \)
- Length of the platform = Length of the train + \( \frac{2}{3} \times \text{Length of the train} \)
- Length of the platform = \( 360 + \frac{2}{3} \times 360 = 360 + 240 = 600 \) meters

### Step 6: Calculate the total distance to be covered when crossing the platform
The total distance to be covered when the train crosses the platform is the sum of the lengths of the train and the platform.
- Total distance = Length of the train + Length of the platform = \( 360 + 600 = 960 \) meters

### Step 7: Calculate the time taken by the train to cross the platform
Using the formula: Time = Distance / Speed
- Time = Total distance / Speed of the train
- Time = \( \frac{960}{40} = 24 \) seconds

### Final Answer:
The time taken by the train to cross the platform is **24 seconds**.

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