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Q:

Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 9 hours after they passed each other the ratio of the speeds of the two trains was 

A) 2:1 B) 3:2
C) 4:3 D) 5:4

Answer:   B) 3:2

Explanation:

Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)

Therefore, Ratio of the speeds of two trains =  = 3 : 2

Q:

The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 kmph. Then find the speed of faster train  ?

A) 68 kmph B) 52 kmph
C) 76 kmph D) 50 kmph
 
Answer & Explanation Answer: A) 68 kmph

Explanation:

Let the speed of the faster train be 'X' kmph,
Then their relative speed= X - 48 kmph
To cross slower train by faster train,
Distance need to be cover = (400 + 600)m = 1 km. and
Time required = 180 sec = 180/3600 hr = 1/20 hr.
Time = Distance/Speed
=> 1/20 = 1/(x-48)
X = 68 kmph

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Q:

A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger  ?

A) 10 sec B) 48 sec
C) 36 sec D) 56 sec
 
Answer & Explanation Answer: C) 36 sec

Explanation:

Given speed of jogger = 9 kmph
Speed of train = 45 kmph
As they are in same direction,
Relative speed = 45 - 9 = 36 kmph = 36x5/18 = 10 m/s
Distance = 240 + 120 = 360 mts
Time = distance/speed = 360/10 = 36 sec.

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Q:

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is  ?

A) 1 : 2 B) 3 : 1
C) 4 : 7 D) 3 : 2
 
Answer & Explanation Answer: D) 3 : 2

Explanation:

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27 x meters, and

length of the second train = 17 y meters.

(27 x + 17 y) / (x + y) = 23

=> 27 x + 17 y = 23 x + 23 y

=> 4 x = 6 y

=> x/y = 3/2.

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Q:

How many seconds will a 600 m long train take to cross a man walking with a speed of 7 km/hr in the direction of the moving train if the speed of the train is 67 km/hr ?

A) 29 sec B) 58 sec
C) 36 sec D) 44 sec
 
Answer & Explanation Answer: C) 36 sec

Explanation:

Speed of train relative to man = 67 - 7 = 60 km/hr.
= 60 x 5/18 = 50/3 m/sec.

Time taken to pass the man = 600 x 3/50 = 36 sec.

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Q:

Train K crosses a pole in 30 seconds and train L crosses the same pole in one minute and 20 seconds. The length of train K is three-fourths the length of train L. What is the ratio of the speed of train K to that of train L   ?

A) 1 : 3 B) 2 : 1
C) 3 : 1 D) 1 : 2
 
Answer & Explanation Answer: B) 2 : 1

Explanation:

Given that train K crosses a pole in 30 seconds and train L crosses the same pole in one minute and 15 seconds.

Let the length of train K be Lk and that of train L be Ll

given that Lk = 3/4 Ll

As the train K and L crosses the pole in 30 seconds and 80 seconds respectively,
=> Speed of train K = sk = Lk/30

Speed of train L = sl = Ll/80

Lk = 3/4 Ll
=> sk = 3/4 Ll/(30) = Ll/40

Ratio of their speeds = sk : sl
= Ll/40 : Ll/80

=> 1/40 : 1/80  =  2 : 1

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