Question

Two trains in opposite direction take 20 sec and 30 sec to pass an electric post if both of the train take 23 sec to pass one another what is the ratio of speed of train ?

• A. 5 : 4
• B. 7 : 3
• C. 8 : 5
• D. 7 : 2

Answer 1

Answer:

B. 7 : 3

Key Concepts and Formulas:

• Train Passing a Stationary Object (Pole, Man, Electric Post):

  • When a train passes a stationary object that has negligible length (like an electric post, a pole, or a standing man), the distance covered by the train is equal to its own length.

  • Formula: Distance = Speed × Time. If L is the length of the train and S is its speed, and T is the time taken to pass the object, then L = S × T.

• Two Trains Passing Each Other (Opposite Directions):

  • When two trains move towards each other (in opposite directions), their speeds add up to give the relative speed.

  • The total distance covered for them to completely pass each other is the sum of their individual lengths.

  • Formula: If Train 1 has length L1 and speed S1, and Train 2 has length L2 and speed S2, and they take time T to pass each other, then (L1 + L2) = (S1 + S2) × T.

Step-by-Step Derivation:

• Let S1 be the speed of the first train and L1 be its length.

• Let S2 be the speed of the second train and L2 be its length.

• From the first condition: The first train passes an electric post in 20 seconds.

  • The distance covered by the first train is its own length, L1.

  • Therefore, L1 = S1 × 20.

• From the second condition: The second train passes an electric post in 30 seconds.

  • The distance covered by the second train is its own length, L2.

  • Therefore, L2 = S2 × 30.

• From the third condition: Both trains pass each other in 23 seconds while moving in opposite directions.

  • The relative speed when moving in opposite directions is the sum of their speeds: S1 + S2.

  • The total distance covered for them to pass each other is the sum of their lengths: L1 + L2.

  • Therefore, (L1 + L2) = (S1 + S2) × 23.

• Substitute the values of L1 and L2 into the third equation:

  • (20S1 + 30S2) = (S1 + S2) × 23

  • 20S1 + 30S2 = 23S1 + 23S2

• Rearrange the terms to group S1 and S2:

  • 30S2 - 23S2 = 23S1 - 20S1

  • 7S2 = 3S1

• Find the ratio of their speeds (S1 : S2):

  • Divide both sides by S2 and by 3:

  • S1 / S2 = 7 / 3

  • Hence, the ratio of the speeds of the trains is 7 : 3.