Miscellaneous Question 19
- The length of train $A$ and $B$ are $300 $ $m$ and $360$ $ m$ respectively. When the trains are travelling in opposite directions they take 12 seconds to cross each other (from the moment they meet). When they are travelling in same direction they take 2 minutes 12 seconds to cross each other (from the moment they meet). What is the speed of the faster train? (in $km / hr$ ).
117
90
72
126
108
(Bank of Baroda PO Exam, 25.09.2016)
Show Answer
Correct Answer: 19. (5)
Solution: 19. (5) Speed of the faster train
$=x \ \mathrm{kmph}$ (let)
Speed of slower train $=y $ $\mathrm{kmph}$
In opposite directions, relative speed $=(x-y) $ $\mathrm{kmph}$
In the same direction, relative speed $=(x-y)~\mathrm{kmph}$
According to the question,
$x+y=\frac{300+360}{12}=\frac{660}{12}$
$\Rightarrow x+y=55$ $\quad$ ……..(i)
and, $x-y=\frac{660}{132}$
$\Rightarrow x-y=5$ $\quad$ ……..(ii)
By adding equations (i) and (ii),
$2 x=60$
$\Rightarrow x=30$ $ \mathrm{m} / \mathrm{sec}$
$=\left(\frac{30 \times 18}{5}\right)$ $ \mathrm{kmph}$
$=108\ \mathrm{kmph}$
BETA
