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Problems on Train (Moderate Level)

Description: Bank ssc quant
Number of Questions: 15
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Tags: Bank ssc quant Concept of Trains/Relative Speed Time and Distance
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A train travelling with a uniform speed crosses a 180 m long platform in 16 seconds and a 125 m long platform in 14 seconds. Find the speed of the train.

  1. 17.5 km/hr

  2. 35.5 km/hr

  3. 63 km/hr

  4. 30 km/hr

  5. None of these

Show answer
Correct Option: C
Explanation:

Let the length of the train be x m.

Then, the speed of the train to cross both the platforms is the same. 

(x + 160)/16 = (x + 125)/14 

After solving, we get

x = 120 m

So, the speed of the train is (120 + 160)/16 = 35/2 m/s = (35/2) * (18/5) = 63 km/hr.

A train crosses two persons travelling at the rates of 6 km/hr and 8 km/hr in the same direction in 12 sec and 16 sec, respectively. Find the speed of the train.

  1. 14 km/hr

  2. 20 km/hr

  3. 16 km/hr

  4. 24 km/hr

  5. None of these

Show answer
Correct Option: A
Explanation:

Let the speed of the train be x km/hr. So, speed of the train with first person in the same direction = (x - 6) km/hr  And speed of the train with second person in the same direction = (x - 8) km/hr So, the length of the train = (x - 6) * 12/60 = (x - 8) * 16/60 After solving, we get  x = 14 So, speed of the train = 14 km/hr

A train passes a platform and a man standing on the platform in 24 seconds and 10 seconds, respectively. If the speed of the train is 72 km/h, then find the length of the platform.

  1. 480 m

  2. 380 m

  3. 280 m

  4. 580 m

  5. None of these

Show answer
Correct Option: C
Explanation:

Speed of the train (V) = 72 km/h = 72 * 5/18 = 20 m/s 

Length of the train = L m and length of the platform = l m 

Time taken by the train to cross the man is 10 seconds. 

So, t = L/V 

10 = L/20

L = 200 m 

Now, time taken by the train to cross the platform is 24 seconds. 

So, t = (L + l)/V 

24 = (200 + l)/20 

l = 280 m

So, the length of the train is 280 m.

A train crosses a man standing on a 140 m long platform in 5 seconds and crosses the platform completely in 15 seconds. Find the length and speed of the train.

  1. 84 m, 50.4 km/h

  2. 70 m, 50.4 km/h

  3. 84 m, 54 km/h

  4. 72 m, 60.4 km/h

  5. None of these

Show answer
Correct Option: B
Explanation:

Let the length of the train be L m and the length of the platform be l m.

Let the speed of the train be V km/h.

The train crosses the platform in 15 seconds. 

So, t = (L + l)/V 

15 = (L + 140)/V -------------------------(1),

Now,the train crosses the man in 5 seconds. 

So, t = L/V

5 = L/V

L = 5V ---------------------------------(2),

From (1) and (2),

V = 14 m/s = 14 * 18/5 = 50.4 km/h

Now, putting the value of "V" in equation (2), we get

L = 5V 

L = 5*14 

L = 70 m 

So, the length and speed of the train are 70 m and 50.4 km/h, respectively.

A train overtakes two persons who are walking in the same direction in which the train is running, at the rates of 3 kmph and 5 kmph, and passes them completely in 10 and 12 seconds, respectively. Find the length of the train.

  1. 70 m

  2. 50 m

  3. 60 m

  4. 75 m

  5. None of these

Show answer
Correct Option: D
Explanation:

Let the speed of the train be x m/s.

Then, speed of the train in the same direction with respect to first person = x - 3 * 5/18 = (x - 5/6) m/s 

Now, speed of the train in the same direction with respect to second person = x - 5 * 5/18 = (x - 25/18) m/s 

So, length of the train is (x - 5/6) * 10 = (x - 25/18) * 25/18.

After solving, we get

x = 25/3 m/s

So, the speed of the train is 25/3 m/s,

Then, length of the train is (25/3 - 5/6) * 10 = 75 m.

A train running at 24 km/h takes 12 seconds to pass a platform. Next, it takes 8 seconds to pass a man walking at 8 km/h in the same direction. Find the length of the platform and the length of the train.

  1. 30 m, 40 m

  2. 30 m, 60 m

  3. 44 m, 36 m

  4. 55 m, 30 m

  5. None of these

Show answer
Correct Option: C
Explanation:

Let the length of the train be L m. 

Let the length of the platform be l m.

Speed of the train (V) = 24 km/h = 24 * 5/18 = 20/3 m/s

Speed of the man (v) = 8 km/h = 8 * 5/18 = 20/9 m/s

The train takes 8 seconds to pass the man. 

So, t = L/(V - v) 

8 = L/(20/3 - 20/9) 

L = 320/9

L = 35.55 m = 36 m (approximately) 

So, length of the train = 36 m 

Now, the train takes 12 seconds to cross the platform. 

So, t = (L + l)/V 

12 = (320/9 + l)/(20/3) 

l = 400/9

l = 44.44 m = 44 m (approximately) 

So, the length of the platform is 45 m and that of the train is 36 m.

Two trains of lengths 360 m and 540 m are running in opposite directions on parallel tracks. If their speeds are 45 km/h and 36 km/h, respectively, then in what time will they cross each other?

  1. 30 seconds

  2. 40 seconds

  3. 20 seconds

  4. 50 seconds

  5. None of these

Show answer
Correct Option: B
Explanation:

Length of the first train (L) be 360 m

Length of the second train (l) = 540 m

Speed of the first train (V) = 45 km/h = 45 * 5/18 = 25/2 m/s

Speed of the second train (v) = 36 km/h = 36 * 5/18 = 10 m/s

So, the required time to cross each other is,

t = (L + l)/(V + v) 

t = (360 + 540)/(25/2 + 10)

t = 40 seconds

Two trains are running in the same direction at 50 km/h and 30 km/h. The faster train crosses a man in the slower train in 30 seconds. Find the length of the faster train.

  1. 168 m

  2. 180 m

  3. 167 m

  4. 200 m

  5. None of these

Show answer
Correct Option: C
Explanation:

The man is in the slower train, so the speed of the slower train is equal to the speed of the man.

Now, let the speed of the faster train be L m.

So, using the following formula:

t = L/( V - v)

30 = L/((50 - 30) * 5/18)

L = 166.6 

L = 167 m So, the length of the faster train is 167 m.

A train running with a speed of 108 km/h crosses a bridge in 5 seconds. Another train, 70 m shorter, crosses the same bridge at 72 km/h. Find the time taken by the second train to cross the bridge.

  1. 7 seconds

  2. 3 seconds

  3. 6 seconds

  4. 4 seconds

  5. None of these

Show answer
Correct Option: D
Explanation:

Let the length of the first train be L m.

Length of the second train = (L - 70) m

And length of the bridge = x m 

Speed of first train (V) = 108 km/h = 108 * 5/18 = 30 m/s

Speed of second train (v) = 72 km/h = 72 * 5/18 = 20 m/s

Now,

t = (L + x)/V 

5 = (L + x)/30 

L + x = 150 -------------------------(1)

Similarly,

t = (L - 70 + x)/20 ----------------(2) 

Now, putting the value of (L + x) in (2), we get

t = (150 - 70)/20 

t = 4 seconds

A train, 60 m long, overtakes a man who is walking at the rate of 9 km/h and crosses him in 4 seconds. Again, the train overtakes another person in 4.8 seconds. At what rate is the second person travelling?

  1. 18 km/h

  2. 12 km/h

  3. 10 km/h

  4. 8 km/h

  5. None of these

Show answer
Correct Option: A
Explanation:

Let the length of the train (L) be 60 m.

Speed of the train = V km/h

Speed of the first man (v1) = 9 km/h = 9 * 5/18 = 5/2 m/s

Let the speed of the second man be v2.

Now, 4 seconds are taken by the train to cross the first person.

t = L/(V - v1) 

4 = 60/(V - 5/2)

V = 35/2

So, the speed of the train is 35/2 m/s. 

Now, time taken by the train to cross the second person is 4.8 seconds.

Then, t = L/(V - v2) 

4.8 = 60/(35/2 - v2) 

v2 = 5 m/s = 5 * 18/5 = 18 km/h, so the speed of the second person is 18 km/h.

A train crosses 100 m and 60 m long tunnels in 12 seconds and 8 seconds, respectively. Find the length and speed of the train.

  1. 20 m, 36 km/h

  2. 35 m, 54 km/h

  3. 40 m, 72 km/h

  4. 50 m, 90 km/h

  5. None of these

Show answer
Correct Option: A
Explanation:

Let the speed of the train be V km/h.

Length of the train be L m.

Length of the first tunnel = T m 

Length of the second tunnel = t m

The train crosses the first tunnel in 12 seconds, so

t = (L + T)/V

12 = (L + 100)/V

12V - L = 100 --------------------(1) 

Similarly, 8 = (L + 60)/V 

8V - L = 60 -----------------------(2) 

From (1) and (2),

V = 10 m/s = 36 km/h 

Now, putting the value of V in equation (1),

12V - L = 100

12(10) - L = 100

L = 20 m

So, length of the train is 20 m and speed is 36 km/h.

Two trains, 175 m and 225 m long, are running in opposite directions at 36 km/h and 54 km/h, respectively. In how much time will they cross each other?

  1. 18 seconds

  2. 16 seconds

  3. 20 seconds

  4. 22 seconds

  5. None of these

Show answer
Correct Option: B
Explanation:

Speed of the first train (V) = 36 km/h = 36 * 5/18 = 10 m/s

Speed of the second train (v) = 54 km/h = 54 * 5/18 = 15 m/s

So, the time required to cross each other is, t = (L + l)/(V + v) 

t = (175 + 225)/(10 + 25) 

t = 16 seconds So, the required time is 16 seconds.

A train, running at a speed of 96 km/h, crosses a man running at a speed of 6 km/h in the opposite direction in 3 seconds. Find the length of the train.

  1. 170 m

  2. 255 m

  3. 340 m

  4. 85 m

  5. None of these

Show answer
Correct Option: D
Explanation:

Let the length of the train be L m.

Speed of the train (V) = 96 km/h = 96 * 5/18 = 80/3 m/s

Speed of the man (v) = 6 km/h = 6 * 5/18 = 5/3 m/s

Now, by using this shortcut formula,

t = L/(V + v) 

3 = L/(80/3 + 5/3)

L = 85 m, so length of the train is 85 m.

A train, 260 m long, meets a man going in the opposite direction running at 8 km/h. The train passes the man in 20 seconds. Find the speed of the train.

  1. 38 km/h

  2. 38.5 km/h

  3. 40 km/h

  4. 40.5 km/h

  5. None of these

Show answer
Correct Option: B
Explanation:

Length of the train (L) = 260 m

Speed of the man (v) = 8 km/h = 8 * 5/18 = 20/9 m/s

Speed of the train = V km/h

So, t = L/(V + v)

20 = 260/(V + 20/9)

= 97/9 m/s

= (97/9) * (18/5) = 38.5 km/h

Two trains, 140 m and 110 m long, are going in the same direction. The faster train takes 50 seconds to pass the other train completely. If they are moving in opposite directions, they pass each other completely in 5 seconds. Find the speed of both the trains.

  1. 99 km/h, 81 km/h

  2. 55 km/h, 45 km/h

  3. 90 km/h, 80 km/h

  4. 72 km/h, 54 km/h

  5. None of these

Show answer
Correct Option: A
Explanation:

Length of the faster train (L) = 140 m

Length of the slower train (l) = 110 m

Speed of the faster train = V km/h 

Speed of the slower train = v km/h 

Now, by using the formula,

t = (L +l)/(V - v) 

50 = (140 + 110)/(V - v) 

V - v = 5 ----------------(1) 

Similarly,

t = (L + l)/(V + v) 

5 = (140 + 110)/(V + v) 

V + v = 50 -----------------(2) 

From (1) and (2),

V = 55/2 = (55/2) * (18/5) = 99 km/h

v = (45/2) * (18/5) = 81 km/h So, the speed of the faster train is 99 km/h and the speed of the slower train is 81 km/h.

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