Question

The given question consists of a set of statements. Find out whether the data provided in the statements are sufficient to answer the question and mark the option:

What is the speed of the train whose length is 105 metres?
I. The train crosses a goods train of 150 metres length running in opposite direction in 5 seconds.
II. The train crosses the same goods train running in the same direction at the speed of 30 km/hr in 15 seconds.

• A. if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
• B. if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
• C. if the data either in Statement I or in Statement II alone are sufficient to answer the question.
• D. if the data even in both Statements I and II together are not sufficient to answer the question.
• E. if the data in both Statements I and II together are necessary to answer the question.

Answer 1

The correct option is E

if the data in both Statements I and II together are necessary to answer the question.

Time taken to cross the train, running in opposite directions $=\frac{(l_1+l_2)}{\left(u+v\right)}sec.$

$\Rightarrow 5=\frac{\left(105+150\right)}{\left(u+v\right)}\Rightarrow u+v=25.5$

Time taken to cross the train, running in same direction $=\frac{(l_1+l_2)}{\left(u-v\right)}sec.\Rightarrow 15=\frac{\left(105+150\right)}{\left(u-30\times \frac{5}{18}\right)}\Rightarrow u=\left(\frac{76}{3}\right)m/sec$

Thus, u and v can be obtained.