A train passes two bridges of lengths 800 m and 400 m in 100 seconds and 60 seconds respectively. What is the length of the train?

Appeared in: AIIMS Rishikesh & Jodhpur NO - 2017

Explanation

The core principle is that the train's speed is constant when crossing both bridges.
The total distance the train travels to cross a bridge is the sum of its own length (L) and the bridge's length.
By setting up two equations for speed [Speed = (L + 800)/100 and Speed = (L + 400)/60] and equating them, we can solve for the single unknown variable, L.
The algebraic simplification leads to 3(L + 800) = 5(L + 400), which resolves to 2L = 400, giving L = 200 m.

Option A: This value is incorrect and likely results from an arithmetic error during the algebraic manipulation, such as incorrectly subtracting the constants (e.g., 2400 - 2000 = 400) or variables (5L - 3L = 2L).
Option B: This is an incorrect value. An error in cross-multiplication or in isolating the variable 'L' would lead to such an answer. For example, an error like 3L + 2400 = 5L + 2000 -> 2L = 400 -> L=200.
Option D: This incorrect answer could arise from a mistake in setting up the initial proportion or an error in the cross-multiplication step. For instance, incorrectly simplifying the time ratio might lead to this result.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of the length of a moving object based on time, speed, and distance as background academic context rather than a clinical decision trigger.
This question tests basic aptitude in algebra and physics (speed, distance, time), a skill required for the non-nursing sections of various competitive nursing entrance exams.
The ability to formulate and solve linear equations is a foundational analytical skill applicable in many fields, including dosage calculations in nursing.
What if the train took less time to cross the longer bridge? If the time to cross the 800m bridge was 60s and the 400m bridge was 100s, the calculation would result in a negative length, which is physically impossible. This highlights the importance of logical consistency in problem-solving.

How to Approach the Question

First, identify the unknown variable you need to find: the length of the train (let's call it 'L').
Recognize the key constant in the problem: the train's speed ('S') is the same in both scenarios.
Recall the formula for an object crossing a platform or bridge: Speed = (Length of Object + Length of Platform) / Time.
Set up two separate equations for the two bridges: S = (L + 800) / 100 and S = (L + 400) / 60.
Since 'S' is the same in both equations, set the two expressions equal to each other: (L + 800) / 100 = (L + 400) / 60.
Solve the resulting algebraic equation for 'L' through simplification and cross-multiplication.

Concept Tested & Keywords

Concept Tested: Calculation of the length of a moving object based on time, speed, and distance.
Stem keywords: train, bridges, length, 800 m, 400 m, 100 seconds, 60 seconds
Lead-in keywords: What is

QWV6JSsm1AygS7pgJctrPg

Practise the full AIIMS Rishikesh & Jodhpur NO - 2017

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