Question:medium

Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6km/hr less than the faster one, its length, in m, is

Updated On: Jan 15, 2026
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The Correct Option is C

Solution and Explanation

The faster train, measuring 160 meters in length, traverses a lamppost in 12 seconds.

Step 1: Calculate the speed of the faster train

The speed of the faster train is calculated as: \[ \text{Speed of faster train} = \frac{160}{12} = \frac{40}{3} \, \text{m/s} \]

Step 2: Calculate the speed of the slower train

The speed of the slower train is determined to be: \[ \text{Speed of slower train} = \frac{40}{3} - \left(6 \times \frac{5}{18}\right) = \frac{35}{3} \, \text{m/s} \]

Step 3: Determine the relative speed when traveling in opposite directions

When the two trains move in opposing directions, their relative speed is the sum of their individual speeds: \[ \text{Relative speed} = \frac{40}{3} + \frac{35}{3} = 25 \, \text{m/s} \]

Step 4: Calculate the length of the slower train

The trains pass each other in 14 seconds. The combined length of both trains is the sum of their individual lengths. Let \( x \) represent the length of the slower train. The relative speed is related to the total length and crossing time by the formula: \[ \text{Relative speed} = \frac{\text{Total length of two trains}}{\text{Time taken to cross each other}} \] Substituting the known values yields: \[ \frac{160 + x}{25} = 14 \] Solving for \( x \): \[ 160 + x = 14 \times 25 = 350 \] \[ x = 350 - 160 = 190 \, \text{meters} \]

Final Answer:

The slower train measures \( \boxed{190} \, \text{meters} \) in length.

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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.
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