A train moves past a telegraph post and a bridge 264...

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A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

A. 69.5 km/hr

B. 70 km/hr

C. 79 km/hr

D. 79.2 km/hr

Answer: Option D

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{length}}\,{\text{of}}\,{\text{the}}\,{\text{train}}\,{\text{be}}\,x\,{\text{metres}} \cr & \,{\text{and}}\,{\text{its}}\,{\text{speed}}\,{\text{by}}\,y\,{\text{m/sec}} \cr & {\text{Then}},\,\frac{x}{y} = 8\,\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 8y \cr & {\text{Now}},\,\frac{{x + 264}}{{20}} = y \cr & \Rightarrow 8y + 264 = 20y \cr & \Rightarrow y = 22 \cr & \therefore {\text{Speed}} = 22\,{\text{m/sec}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {22 \times \frac{{18}}{5}} \,{\text{km/hr}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 79.2\,{\text{km/hr}} \cr} $$

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Comments (3)

Sanjeevini O:

2 years ago

Let the length of train be d
Then speed=distance/time
Speed=d/8
Time=distance/speed
20=(264+d)/d/8
20=((264+d )*8)/d
20d=264*8+8d
20d-8d=2112
12d =2112
d=2112/12
d=176m
Speed=distance/time
Speed=176/8
Speed=22m/s
Speed in kmph=22*18/5=79.2kmph
Farukh Mansoor:

6 years ago

Let length of train = x

post is like a point which means to cross the post by train it takes 'x' metres in 8 seconds
So, Speed while crossing post = x/8 m/s

Bridge length = 264 m
time to cross = 20 sec
For train to cross the bridge completely = (264+x) m
Speed while crossing bridge = (264+x) / 20 m/s

Speed while crossing post = Speed while crossing bridge
x / 8 = (264+x) / 20
20x = 8*(x+264)
20x = 8x + 2112
12x = 2112
x = 2112 / 12
x = 176 m

Length of train is 176 m.

Speed = x / 8 = 176 / 8 = 22m/s = = 79.2 km/h
MD Rakib:

7 years ago

TIME DIFFERENCE=20-8=12
S=264/12=22*18/5=79.2KMPH