Correct Answer: 78. (1)

Solution: 78. (1) Trains are running in opposite directions.

If speed of one train be $x $ $\mathrm{m} /$ sec.

Then, speed of other train $=\frac{5 x}{2} $ $\mathrm{m} / \mathrm{sec}$.

$\therefore$ Relative speed $=x+\frac{5 x}{2}$

$=\frac{7 x}{2} $ $\mathrm{m} / \mathrm{sec}$.

According to the question,

Relative speed $=\frac{\text { Total length of both trains }}{\text { Time taken in crossing }}$

$\Rightarrow \frac{7 x}{2}=\frac{300}{12}=25$

$\Rightarrow x=\frac{25 \times 2}{7}$

$=\frac{50}{7}$ metre $/$ second

$\therefore$ Speed of faster train

$=\left(\frac{5}{2} \times \frac{50}{7} \times \frac{18}{5}\right) $ $\mathrm{kmph}$.

$\approx 64 $ $\mathrm{kmph}$.