__Practice Problems on Trains – Set 1__**1. A train of length 150 meters can cross a bridge in 30 seconds when travelling at a speed of 40km/hr. Then what is the length of the bridge?**

a) 180m

b) 182

c) 183

**Answer:**

**C)**

**Explanation:**

Let the length of the bridge be X.

The speed of the train = 40km/hr = 40 x 5/18 m/sec =
100/9 m/sec.

The time taken to cross the bridge = 30 seconds.

Then, [150 + X ] / 30 = 100/9

150 + X = 3000 /9

X = 3000/9 - 150 = 1650/9 = 183.33

Hence the answer is 183 m.

**2.**

**Two trains 300m and 400m long run at the speeds of 40 kmph and 50kmph respectively in opposite Directions on parallel tracks. The time taken to cross each other?**

a)
20 sec

b)
25 sec

c)
26 sec

d)
28 sec

**Answer:**

**D)**

**Explanation:**

Length of two Trains = 300m + 400m = 700m

Total Speed= 40 Kmph + 50 Kmph (Opposite Direction) =
90 Kmph

Time = Distance/Speed

Time = 700/ 90

Time = 28Sec

**3. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train ?**

a) 230 m

b) 240 m

c) 260 m

d) 320 m

**Answer:**

**A)**

**Explanation:**

Relative speed = (120 + 80) km/hr = 200 kmph = 200 ×
5/18 = 500/9 mph

Let the length of the other train be x metres.

Then, (270 + x)/9 = 500/9 => x = 500 – 270 = 230

**4. Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:**

a) 58 sec

b) 50 sec

c) 48 sec

d) 56 sec

**Answer:**

**C)**

**Explanation:**

Relative speed = all lengths/time

[60+90] = [1.10 +0.9 ]/time [ PLUS when opposite
direction] time=2/150 = 1/75 h

1 hour______3600 sec

1/75 hr______?

?= 3600/75=48 sec

**5. A train crosses a bridge and a bike standing on the bridge in 40 seconds, 25 seconds respectively. What is the length of the bridge if the speed of the train is 50.4km/hr?**

a) 180m

b) 210

c) 183

d) 185

**Answer:**

**B)**

**Explanation:**

Given that,

The speed of the train = 50.4km/hr = 50.4 x 5/18
m/sec = 14 m/sec

The train crosses a bike(standing object) in 25
seconds.Then,

Length of the train = (14 x 25)m = 350 m.

Now, let the length of the bridge is X m.

the train crosses the bridge in 40 seconds.

Then, (X + 350)/40 = 14

X + 350 = 14 x 40 = 560

X = 210

Hence the bridge is 210m long.

**6. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:**

a) 45m

b) 55m

c) 50m

d) 60m

**Answer:**

**C)**

**Explanation:**

2 kmph = (2 x 5/18) m/sec = 5/9 m/sec.

4 kmph = (4 x 5/18 m/sec = 10/9 m/sec.

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

Then, ( x/(y - 5) = 9 and ( x/(y - 10) = 10.

Therefore 9y - 5 = x and 10(9y - 10) = 9x

=> 9y - x = 5 and 90y - 9x = 100.

On solving, we get: x = 50.

**7. 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 kmph

b) 70 kmph

c) 72 kmph

d) 79.2 kmph

**Answer:**

**D)**

**Explanation:**

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

Then, x/y = 8 => x = 8y

Now, (x + 264)/20 = y

=> 8y + 264 = 20y

=> y = 22.

Speed = 22 m/sec = 22 × 18/5km/hr = 79.2 km/hr.

**8. A train travelling at a speed of 75 mph enters a tunnel 7/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?**

A) 1 min

B) 3 min

C) 5 min

D) 6 min

**Answer:**

**B)**

**Explanation:**

Actually train is covering length of tunnel + its
own length here

so total distance = 7/2 + 1/4= 15/4 miles

time= distance /speed

time= (15/4) / 75 = 1/20 hour

(1/20)x60 = 3 min

**9. The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?**

A) 10:30 am

B) 10:45 am

C) 11 am

D) 11:25 am

**Answer:**

**C)**

**Explanation:**

Suppose they meet x hrs after 8 a.m.

Then, (Distance moved by first in x hrs) + [Distance
moved by second in (x-1) hrs] = 330

60x + 75(x – 1) = 330

x = 3

So, they meet at (8 + 3), i.e. 11 a.m

**10. A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?**

a) 96 kmph

b) 81 kmph

c) 51 kmph

d) 62 kmph

**Answer:**

**B)**

**Explanation:**

4.5 km/hr = ( 4.5 x 5/18 ) m/sec = 5/4 m/sec = 1.25
m/sec, and

5.4 km/hr = ( 5.4 x 5/18 ) m/sec = 3/2 m/sec = 1.5
m/sec.

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

Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5

=> 8.4x - 10.5 = 8.5x - 12.75

=> 0.1x = 2.25

=> x = 22.5

Therefore Speed of the train = ( 22.5 x 18/5 ) km/hr
= 81 km/hr.