Question

A train running at a certain speed crosses a platform in $30$ seconds. What is the speed of the train?
I. Length of the train is $240$ m.
II. The train crosses a man who is on the platform in $12$ seconds. 

• A. If I alone is sufficient but II alone is not sufficient.
• B. If II alone is sufficient but I alone is not sufficient.
• C. If either I alone or II alone is sufficient.
• D. If even I + II together are not sufficient.
• E. If I + II together are necessary to answer the question.

Hint:

When a train "crosses a platform", use $(L+P)/v$; when it “crosses a man”, use $L/v$. Often, length + one more time measurement together fix the speed.

Answer 1

Answer: (E)

Step 1: From statement II, the time to pass a stationary man equals \( \dfrac{L}{v}=12 \), so \( v=\dfrac{L}{12} \); this alone still has two unknowns.

Step 2: From statement I, \( L=240 \) m. Substituting into the relation from Step 1, \[ v=\frac{240}{12}=20 \text{ m/s}. \]

Step 3: Neither statement alone gives a numerical speed, but combining them fixes \( v \) uniquely, so both statements together are necessary.
\[ \boxed{\text{I + II together necessary}} \]