Lakshya Education MCQs

Question:

A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:

Options:
 A. 130 B. 360 C. 500 D. 540

Speed =$$\left(78\times\frac{5}{18}\right)m/sec = \left(\frac{65}{3}\right)m/sec.$$

Time = 1 minute = 60 seconds.

Let the length of the tunnel be x metres.

Then,$$\left(\frac{800+x}{60}\right) = \frac{65}{3}$$

3(800 + x) = 3900

x = 500.

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More Questions on This Topic :

Question 1.

A train travelling at a speed of 75 mph enters a tunnel $$3^{\frac{1}{2}}$$miles long. The train is$$\frac{1}{4}$$mile

Options:
1.    2.5 min
2.    3 min
3.    3.2 min
4.    3.5 min

Total distance covered = $$\left(\frac{7}{2}+\frac{1}{4}\right)miles$$

=$$\frac{15}{4}miles.$$

Thairfor Time taken = $$\left(\frac{15}{4\times75}\right)hrs$$

$$\frac{1}{20}hrs$$

=$$\left(\frac{1}{20}\times60\right)min.$$

= 3 min.

Question 2.

A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

Options:
1.    5 sec
2.    6 sec
3.    7 sec
4.    10 sec

Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

$$\left(66\times\frac{5}{18}\right)m/sec$$

=$$\left(\frac{55}{3}\right)m/sec.$$

Thairfor Time taken to pass the man = $$\left(100\times\frac{3}{55}\right)sec = 6sec.$$

Question 3.

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

Options:
1.    9
2.    9.6
3.    10
4.    10.8

Relative speed = (60 + 40) km/hr = $$\left(100\times\frac{5}{18}\right)m/sec=\left(\frac{250}{9}\right)m/sec$$

Distance covered in crossing each other = (140 + 160) m = 300 m.

Required time = $$\left(300\times\frac{9}{250}\right)sec= \frac{54}{5}sec=10.8sec.$$

Question 4.

A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

Options:
1.    320 m
2.    350 m
3.    370 m

Speed = $$\left(\frac{300}{18}\right)m/sec = \frac{50}{3}m/sec.$$

Let the length of the platform be x metres.

Then, $$\left(\frac{x+300}{39}\right) = \frac{50}{3}$$

3(x + 300) = 1950

x = 350 m.

Question 5.

A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

Options:
1.    50 m
2.    150 m
3.    200 m

Let the length of the train be x metres and its speed by y m/sec.

Then,$$\frac{x}{y} = 15 \Rightarrow y = \frac{x}{15}$$

Thairfor $$\frac{x+100}{25} = \frac{x}{15}$$

15(x + 100) = 25x

15x + 1500 = 25x

1500 = 10x

x = 150 m.

Question 6.

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?

Options:
1.    69.5 km/hr
2.    70 km/hr
3.    79 km/hr
4.    79.2 km/hr
Then, $$\frac{x}{y} = 8 \Rightarrow x = 8y$$
Now,$$\frac{x+264}{20} = y$$
Speed = $$22m/sec = \left(22\times\frac{18}{5}\right)km/hr = 79.2 km/hr$$