Question

A train running at 18 km per hour crosses a mark on the platform in 9 seconds and takes 25 seconds to cross the platform. If P is the length of the train and Q is the length of the platform in meters, then (P, Q) = ___ .

• A. (45, 80)
• B. (45, 75)
• C. (50, 90)
• D. (50, 80)

Answer 1

The Correct Option is A

To solve this problem, we need to determine the lengths of the train \( P \) and platform \( Q \) given the speed of the train and the time it takes to cross a mark on the platform and the platform itself.

1. First, convert the speed of the train from kilometers per hour to meters per second:
   • Speed in km/h = 18 km/h
   • Speed in m/s = \( \frac{18 \times 1000}{60 \times 60} = 5 \, \text{m/s} \)
2. Determine the length of the train \( P \) using the time it takes to cross a mark:
   • Time to cross the mark = 9 seconds
   • The distance covered in this time is the length of the train: \( P = \text{Speed} \times \text{Time} = 5 \times 9 = 45 \, \text{meters} \)
3. Determine the length of the platform \( Q \) using the time it takes to cross the platform:
   • Time to cross the platform = 25 seconds
   • Here, the distance covered is the length of the train plus the length of the platform: \( \text{Total Distance} = \text{Speed} \times \text{Total Time} = 5 \times 25 = 125 \, \text{meters} \)
   • Length of the platform \( Q \) is given by: \( Q = \text{Total Distance} - \text{Length of the Train} = 125 - 45 = 80 \, \text{meters} \)

Thus, the lengths are \( P = 45 \, \text{meters} \) and \( Q = 80 \, \text{meters} \).

Therefore, the correct option is (45, 80).