Each question is followed by two statements I & II. You have to determine…
2025
Each question is followed by two statements I & II. You have to determine which statement(s) is/are necessary/sufficient to answer the question and mark the answer accordingly.
What is the speed of the train?
I. The train can cross a 100 m long platform in 10 sec and a tree in 5 sec.
II. The train can cross another train of the same length, coming from the opposite direction at the same speed, in 20 sec.
Answer: D. Only statement I alone is sufficient to answer. — In a train-crossing problem, crossing a stationary point object (a pole, a person, a tree) means the train covers a distance equal to its own length, while…
- A.
Only statement II alone is sufficient to answer.
- B.
Either statement I or statement II alone is sufficient to answer.
- C.
Both statement I and II together are necessary to answer.
- D.
Only statement I alone is sufficient to answer.
- E.
Neither statement I nor statement II is sufficient to answer.
Attempted by 13 students.
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Correct answer: D
In a train-crossing problem, crossing a stationary point object (a pole, a person, a tree) means the train covers a distance equal to its own length, while crossing an extended object (a platform, a bridge) means it covers its own length plus that object's length. In a Data Sufficiency question, a statement is sufficient only when the numbers it supplies determine a single, unique value for the unknown being asked — a statement that only fixes a ratio or relation between two unknowns, without pinning either one down, is NOT sufficient.
Let the train's length be L metres and its speed be v m/s.
Crossing the tree (a point object) in 5 sec means the train covers distance L in 5 sec: L = 5v.
Crossing the 100 m platform in 10 sec means the train covers distance (L + 100) in 10 sec: L + 100 = 10v.
Substituting L = 5v into the second relation: 5v + 100 = 10v.
Simplifying: 100 = 5v, so v = 20 m/s (and L = 5 × 20 = 100 m).
Statement II says the train crosses another train of the same length L, moving at the same speed v, from the opposite direction, in 20 sec. The combined length to be crossed is 2L, and since the trains move toward each other, the relative speed is 2v. So 2L ÷ 2v = L/v = 20 — this only fixes the ratio of length to speed, not either value individually, so Statement II alone cannot determine the speed.
Note: solved in isolation, Statement I gives length ÷ speed = 5, while Statement II's own numbers separately imply length ÷ speed = 20. This mismatch between the two statements does not affect the sufficiency verdict — the question only asks whether each statement, taken on its own, supplies enough information to fix the speed, and Statement I's two crossing times already do that without any reference to Statement II.
Cross-check: with v = 20 m/s and L = 100 m, the tree-crossing time is L/v = 100/20 = 5 sec, and the platform-crossing time is (L + 100)/v = 200/20 = 10 sec — both match the given data, confirming the two equations were solved correctly.
Since Statement I alone yields two independent equations that solve uniquely for the speed, while Statement II alone yields only a ratio, only Statement I is sufficient to answer the question.