Question:medium

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

Updated On: Jan 15, 2026

  • 15

  • 12

  • 6

  • 10

Show Solution

The Correct Option is A

Solution and Explanation

1. Given:

  • Train A arrives at station Y 10 minutes after meeting Train B.
  • Train B arrives at station X 9 minutes after meeting Train A.
  • Let the meeting point be M.

2. Let t represent the time (in minutes) each train spent traveling to point M.

Based on the provided information:

  • Train A: Traverses from X to M in \( t \) minutes, then from M to Y in \( 10 - t \) minutes.
  • Train B: Traverses from Y to M in \( t \) minutes, then from M to X in 9 minutes.

Since the distances XM and MY are equal for both trains (as they meet at the same point), the ratio of their travel times is inversely proportional to their speeds:

\[ \frac{t}{9} = \frac{10 - t}{t} \]

3. Equation Solution

Upon cross-multiplication:

\[ t^2 = 9(10 - t) \] \[ t^2 = 90 - 9t \Rightarrow t^2 + 9t - 90 = 0 \]

Solving the quadratic equation:

\[ (t + 15)(t - 6) = 0 \Rightarrow t = -15 \text{ or } t = 6 \]

As time cannot be negative, the valid solution is:

\[ t = 6 \]

4. Conclusion

Train B's travel time:

\[ \text{From Y to M: } t = 6 \text{ minutes} \] \[ \text{From M to X: } 9 \text{ minutes} \] \[ \Rightarrow \text{Total travel time from Y to X = } 6 + 9 = \boxed{15} \text{ minutes} \]

Final Answer: 15 minutes

Was this answer helpful?
12

Top Questions on Time and Work

Questions Asked in CAT exam

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
View Solution