A train crosses a pole in 20 seconds and passes a 200 m long bridge in 36 seconds. How much time (in hours) will it take to cover a distance of 108 km?

Appeared in: RRB Nsg Superintendent -29 April 2025 (Shift-1st)

Explanation

The problem requires calculating the train's speed first, using the two scenarios provided.
In the first scenario (crossing a pole), the distance is the train's length (L), so L = Speed (S) × 20.
In the second scenario (crossing a bridge), the distance is (L + 200), so L + 200 = S × 36.
Solving these two simultaneous equations gives the speed S = 12.5 m/s.
This speed is converted to 45 km/h by multiplying by 18/5.
Finally, the time to cover 108 km is calculated as Distance / Speed, which is 108 / 45 = 2.4 hours.

Option A: This value would result from a miscalculation, such as an error in solving the simultaneous equations for the train's speed or an incorrect conversion between m/s and km/h.
Option B: This is an incorrect result. It likely stems from an arithmetic error during the calculation of the train's speed or in the final division to find the time.
Option D: This value is incorrect and would be the result of a calculation error. For instance, incorrectly dividing 108 by a wrongly calculated speed could lead to this answer.

Visual 1: Infographic. A diagram illustrating the difference in distance covered when a train crosses a stationary point object (like a pole) versus a long object (like a bridge). It would show 'Distance = Length of Train' for the pole and 'Distance = Length of Train + Length of Bridge' for the bridge.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Problems on Trains - Speed, Distance, and Time as background academic context rather than a clinical decision trigger.
This question assesses general aptitude and quantitative reasoning skills, which are part of many competitive nursing entrance exams.
While not directly clinical, strong analytical and mathematical skills are beneficial for nurses in tasks like medication dosage calculation, interpreting lab results, and managing fluid balances.
What if the train took 40 seconds to cross the bridge? The equation would be L + 200 = 40S. Substituting L = 20S gives 20S + 200 = 40S, so 20S = 200, and S = 10 m/s (36 km/h). The time to cover 108 km would then be 108/36 = 3 hours.

How to Approach the Question

First, carefully read the problem and identify the two distinct scenarios provided: the train crossing a pole and the train crossing a bridge.
Define variables for the unknown quantities, typically the length of the train (L) and its speed (S).
Formulate an algebraic equation for each scenario using the fundamental formula: Distance = Speed × Time.
Remember that the distance to cross a point object (pole) is the train's own length (L), while the distance to cross an object with length (bridge) is (L + length of the object).
Solve the resulting system of two equations to find the value of the speed (S).
Pay close attention to units. The speed will be in m/s, but the final question involves km and hours, so a unit conversion is necessary (m/s to km/h is × 18/5).

Concept Tested & Keywords

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Practise the full RRB Nsg Superintendent -29 April 2025 (Shift-1st)

Attempt every question from this paper in a timed mock, then review the full solution for each one.