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)

Let train length $L$, platform length $P$, speed $v$. From the stem, \[ \frac{L+P}{v}=30. \tag{1} \] I alone: $L=240$ gives two unknowns ($P,v$) in (1) $\Rightarrow$ not sufficient.
II alone: time to cross a man $=\dfrac{L}{v}=12 \Rightarrow v=\dfrac{L}{12}$, but $L$ unknown $\Rightarrow$ not sufficient.
I + II: from II, $v=L/12$; with $L=240$, $v=20$ m/s. So speed is determined. Hence (e).