Question

Two trains are travelling on two adjacent tracks. What would be their respective speeds?
Statement 1: The relative speed when the trains are travelling in the same direction is 30 kmph
Statement 2: The relative speed when the trains are travelling in the opposite direction is 90 kmph
Directions: This question has a problem and two statements numbered (1) and (2) giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Indicate your answer :

• A. statement (1) alone is sufficient to answer the question
• B. statement (2) alone is sufficient to answer the question
• C. both the statements together are needed to answer the question
• D. either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is C

To determine the speeds of the two trains, we need to understand and utilize the concept of relative speed. We have two scenarios based on the problem:

• Statement 1: The relative speed when the trains are traveling in the same direction is 30 kmph.
• Statement 2: The relative speed when the trains are traveling in the opposite direction is 90 kmph.

Let's define:

• \(S_1\): Speed of train 1 (kmph)
• \(S_2\): Speed of train 2 (kmph)

Analyzing the Statements:

1. When the two trains move in the same direction:
   The relative speed is given by: \(|S_1 - S_2| = 30\)
2. When the two trains move in opposite directions:
   The relative speed is given by: \(S_1 + S_2 = 90\)

Solving the Equations:

We have two equations:

• \(|S_1 - S_2| = 30\) (Equation 1)
• \(S_1 + S_2 = 90\) (Equation 2)

We can solve these equations as follows:

1. From Equation (1), consider two cases:
   • \(S_1 - S_2 = 30\)
   • \(S_2 - S_1 = 30\) (not required as it will contradict the solution)
2. From Equation 2, substitute into \(S_1 + S_2 = 90\)
   • Adding Equations gives:
   • Substituting back gives:

Conclusion:

Both statements together provide enough information to uniquely determine the speeds of the two trains:

• Train 1: \(60 \text{ kmph}\)
• Train 2: \(30 \text{ kmph}\)

Therefore, the correct answer is that both the statements together are needed to answer the question.