Question:medium

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 :

Updated On: Jan 13, 2026
  • statement (1) alone is sufficient to answer the question
  • statement (2) alone is sufficient to answer the question
  • both the statements together are needed to answer the question
  • either statement (1) alone or statement (2) alone is sufficient to answer the question
  • neither statement (1) nor statement (2) suffices to answer the question
Show Solution

The Correct Option is C

Solution and Explanation

The correct answer is option (C):
both the statements together are needed to answer the question

The correct answer is: both the statements together are needed to answer the question.

Here's the breakdown:

The problem asks for the individual speeds of the two trains. We're given information about their relative speeds in two different scenarios: when they're traveling in the same direction and when they're traveling in opposite directions.

Let's denote the speeds of the two trains as 'x' and 'y' (in kmph).

Statement 1: The relative speed when traveling in the same direction is 30 kmph. This translates to the equation: |x - y| = 30. We don't know which train is faster, so we use the absolute value.

Statement 2: The relative speed when traveling in the opposite direction is 90 kmph. This translates to the equation: x + y = 90.

Alone, neither statement allows us to determine the values of x and y.

However, if we use both statements together, we can solve for x and y.

We have two possibilities from Statement 1:

Case 1: x - y = 30
Case 2: y - x = 30

For Case 1 (x - y = 30): We also have x + y = 90. Adding these two equations gives 2x = 120, therefore x = 60 kmph. Substituting this into either equation gives y = 30 kmph.

For Case 2 (y - x = 30): We also have x + y = 90. Adding these two equations gives 2y = 120, therefore y = 60 kmph. Substituting this into either equation gives x = 30 kmph.

In either case, knowing both relative speeds allows us to determine the individual speeds of the trains. Therefore, both statements are needed.
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