Miscellaneous Question 21
- At its usual speed, a 150 metre long train crosses a platform of length $L$ metres in 24 seconds. AT $75 \%$ of its usual speed, the train crosses a vertical pole in 12 seconds. What is the value of $L$ ?
(1) 250
(2) 225
(3) 240
(4) 260
(5) 280
Show Answer
Correct Answer: 21. (1)
Solution: 21. (1) Usual speed of train
Length of train and platform
$=$ Time taken in crossing
$=\left(\frac{150+\mathrm{L}}{24}\right) \mathrm{m} / \mathrm{sec}$.
Case II,
$75 \%$ of $\left(\frac{150+\mathrm{L}}{24}\right)$
$=\frac{\text { Length of train }}{\text { Time taken in crossing }}$
$\Rightarrow\left(\frac{150+\mathrm{L}}{24}\right) \times \frac{3}{4}=\frac{150}{12}$
$\Rightarrow(150+\mathrm{L})=\frac{150}{12} \times \frac{24 \times 4}{3}$
$\Rightarrow 150+\mathrm{L}=400$
$\Rightarrow \mathrm{L}=400-150=250$ metre
BETA
