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# Problems on Trains Questions

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A train runs at a speed of 42 m/s and takes 35 seconds to pass a tunnel. After travelling some distance it takes 15 seconds to pass a pole. What is the length of the tunnel?

A162m

B630m

C840m

D240m

Explanation:

Length of tunnel+length of train = 42*35 m
Length of train = 42*15 m
Length of tunnel = 42*35 m - 42 *15 m = 42 *(35-15)m = 840 m

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A long distance train is scheduled to reach its destination in 19 hours. After 10 hours of journey, due to disruption of rail traffic, the train has to be stationed for 1 hour. If the average speed of the train is 100km/hr, at what speed should it travel to cover the distance in same amount of time?

A110 km/hrs.

B110.5 km/hrs.

C112.5 km/hrs.

D112 km/hrs.

Explanation:

Total distance = 100*19=1900 km.
Distance travelled in 10 hr = 1000 km.
Remaining distance = 900 km.
So, speed = 900/(19-11)= 112.5km/hr

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Two trains 246 m and 304 m long are travelling towards one another at 114 km/hr and 66 km/hr respectively. How long do the trains take to pass one another?

A13 sec

B1 sec

C11 sec

D9 sec

Explanation:

114 km/h => 114*5/18 m/s => 95/3 m/s
66km/h => 66*5/18 m/s => 55/3 m/s
Time taken = (246+304)/(55/3 + 95/3) => 11 sec

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Two stations Ahmedabad and Baroda are 100 kms apart. Navjeevan Express travelling at 50 kmph leaves Ahmedabad at 6.30 AM and Howrah-Ahmedabad Express travelling at 40 kmph leaves Baroda at 7 AM. At 7.30 AM Mr. Shah, the traffic controller, discovers that both the trains are travelling on the same line. How much time is available to avert an accident?

A15 min.

B20 min.

C25 min.

D30 min.

Explanation:

Let A, B and C be the points for the first train to start, second train to start and the trains to meet respectively. Distance travelled by first till 7:30 = 50 * 1 = 50.
Distance travelled by second till 7:30 = 40 * 0.5 = 20.
Remaining distance = 100 - 50 - 20 = 30.
Time available = [30/(50 + 40)] hrs. = 1/3 hrs. = 20 min.

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The speed of a railway engine is 42 kilometres per hour, with no compartment attached to it. The speed of the engine reduces directly as the square root of the number of compartments attached to it. The speed of the engine is 24 kilometres per hour with 9 compartments attached. Find out the maximum number of compartments with which the engine can still move.

A49

B48

C46

D47

Explanation:

Solution:

Let Speed is the function of K1, K2 and n. K1 and K2 are constant and n is the no. of compartments.

Speed varies as,

S = K1 â€“ (K2*(n)^1/2)

S = 42 when n= 0 and K1 = 42

S= 24 when n = 9 So K2 = 6

Now, S become,

S = 42 -6(n)^1/2  it must be > 0 (always).

So, n should be maximum which is less than 49, hence n = 48.

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A train 575 m long crosses a tunnel of length 325 in 90 sec. What is the speed of the train in kmph.

A28

B32

C36

D24

Explanation:

Total distance traveled = Length of train + Length of tunnel
= 575 + 325 = 900.
Time taken to cross the tunnel = 90 sec.
Speed in kmph = distance/time * 18/5 = 900/90 * 18/5 = 180/5 = 36 kmph.

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2 hours after a freight train leaves Delhi a passenger train leaves the same station travelling in the same direction at an average speed of 16 km/hr. After travelling 4 hrs the passenger train overtakes the freight train. The average speed of the freight train was?

A30 km/hr

B10.67 km/hr

C58 km/hr

DNone of these

Explanation:

Solution:

Let the speed of the freight train be x km/hr

And the speed of the passenger train is 16 km/hr.................. (given)

Now the passenger train overtakes the freight train after 4 hrs, so the freight train by this time would have travelled for 6 hrs(2hrs 4hrs).since we know that passenger train starts after 2hrs.

therefore distance travelled by freight train in 6hrs = distance travelled by passenger train in 4hrs( as they meet)

x*6=16*4

6x=64

x=10.67 km/hr

therefore the speed of freight train is 10.67 km/hr

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Two trains with lengths x and y ,and speeds u and v. Approaching each other how much time it takes to takes for faster train to cross other train?

Given: u > v and x > y

A(x + y)/(u - v) sec.

B(x - y)/(u + v) sec.

C(x + y)/(u + v) sec.

DNone of these

Explanation:

By the formula time=distance/speed.

but, we have two trains with two different distances and speeds.

then we use the formula,

total time = [(Distance1) + (Distance2)]/[speed1 + speed2]

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