# CRE 3 - Trains | Arithmetic - Time, Speed & Distance

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

A train 150 meters long, running with a speed of 30 km/h will pass a standing man in (in seconds):

- (a)
18

- (b)
45

- (c)
12

- (d)
5

Answer: Option A

**Explanation** :

Speed of train = (30 × 5/18) = 25/3 m/sec

Required time = (150 × 3)/25 = 18 sec

Hence, option (a).

Workspace:

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

A train 280 meters long is moving at a speed of 60 km/h. The time taken by the train to cross a platform 220 meters long is (in seconds):

- (a)
20

- (b)
25

- (c)
30

- (d)
35

Answer: Option C

**Explanation** :

Speed of train = 60 × 5/18 = 50/3 m/sec

Time taken by the train to cover = (220 + 280) meters = 500 ÷ 50/3 = 30 sec.

Hence, option (c).

Workspace:

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

A train 120 m long, crosses a pole in 10 seconds. The speed of the train is :

- (a)
40 kmph

- (b)
43.2 kmph

- (c)
45 kmph

- (d)
None of these

Answer: Option B

**Explanation** :

Distance covered in one second = 12 m.

∴ Speed = 12 m/sec = 12 × 18/5 = 43.2 km/h.

Hence, option (b).

Workspace:

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

A train running at the rate of 36 km/h passes a standing man in 8 seconds. The length of the train is (in meters):

- (a)
45

- (b)
288

- (c)
80

- (d)
48

Answer: Option C

**Explanation** :

Speed of train = 36 × 5/18 = 10 m/sec

∴ 8 = Length of the train / speed of the train

∴ length of train = 8 × 10 = 80 meters

Hence, option (c).

Workspace:

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

A 400 m long train is travelling at 72 km/hr. If it is 200 m away from the signal, in what time (in sec) will it have completely passed the signal?

Answer: 30

**Explanation** :

72 kmph = 20 m/s

T = D/S = (400 + 200)/20 = 30 secs.

Hence, 30.

Workspace:

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

Two trains, one of length 400 m and other of 200 m, travel at 36 kmph and 72 kmph respectively. These trains are running on parallel tracks. How long will it take them to cross each (in sec) other if the trains are running in opposite direction?

Answer: 20

**Explanation** :

36 kmph = 10 m/s and 72 kmph = 20 m/s

T = D/S = (400 + 200)/(10 + 20) = 600/30 = 20 secs.

Hence, 20.

Workspace:

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

Two trains, one of length 400 m and other of 200 m, travel at 36 kmph and 72 kmph respectively. These trains are running on parallel tracks. How long will it take them to cross each other (in sec) if the trains are running in same direction?

Answer: 60

**Explanation** :

36 kmph = 10 m/s and 72 kmph = 20 m/s

T = D/S = (400 + 200)/(20 - 10) = 600/10 = 60 secs.

Hence, 60.

Workspace:

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

Two trains, one of length 600 m and other of 200 m, travel at 36 kmph and 72 kmph respectively. These trains are running on parallel tracks. How long (in sec) will it take for the slower train to completely cross the driver of the other train if the trains are running in opposite direction?

Answer: 20

**Explanation** :

36 kmph = 10 m/s and 72 kmph = 20 m/s

T = D/S = (600)/(10 + 20) = 600/30 = 20 secs.

Hence, 20.

Workspace:

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is?

- (a)
48 kmph

- (b)
54 kmph

- (c)
66 kmph

- (d)
82 kmph

Answer: Option D

**Explanation** :

Length of first train = 0.108 km

Length of second train = 0.112 km.

Let the speed of second train be x.

As the trains are moving towards each other,

$\frac{0.108+0.112}{50+x}=\frac{6}{60\times 60}$

∴ x = 82 km/hr.

Hence, option (d).

Workspace:

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

A train travelling at 36 kmph crosses a platform in 20 seconds and a man standing on the platform in 10 seconds. What is the length of the platform in meters?

- (a)
240 meters

- (b)
100 meters

- (c)
200 meters

- (d)
300 meters

Answer: Option B

**Explanation** :

Speed of train = 36 kmph = 36 × 5 /18 = 10 m/s

Let the length of the platform be P and length of the train be T.

Now, the train crosses the platform in 20 seconds and the man in 10 seconds.

Hence, the train traveled P + T in 20 seconds and T in 10 seconds.

Hence, it traveled P distance in 20 – 10 = 10 seconds.

Hence, P = 10 × 10 = 100 meters.

Hence, option (b).

Workspace:

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

Two trains starting at the same time from two stations 200 km apart are travelling in opposite directions. They cross each other at a distance of 120 km from one of the stations. The ratio of their speeds will be

- (a)
11 : 10

- (b)
9 : 20

- (c)
11 : 9

- (d)
3 : 2

- (e)
9 : 10

Answer: Option D

**Explanation** :

If 120 km is the distance from one of the stations, the other station is at a distance of 80 km.

Since the time taken to meet will be the same,

Ratio of speeds = ratio of distances = 120 : 80 = 3 : 2

Hence, option (d).

Workspace:

**CRE 3 - Trains | Arithmetic - Time, Speed & Distance**

A man on a platform notices that a train going in one direction takes 10 seconds to pass him and a train of the same length going in the other direction takes 15 seconds to pass him. If the length of the train is 600 m each, what is the time taken by the two trains to pass one another?

- (a)
8 seconds

- (b)
9 seconds

- (c)
11 seconds

- (d)
12 seconds

- (e)
13 seconds

Answer: Option D

**Explanation** :

Speed of train 1 = 600/10 = 60 m/s

Speed of train 2 = 600/15 = 40 m/s

Since they travel in opposite direction,

Therefore, relative speed = 60 + 40 = 100 m/s

Now, time taken to cross each other = $\frac{Lengthoftrain1+Lengthoftrain2}{Relativespeed}$ = $\frac{600+600}{100}$ = 12 secs

Thus, time taken by the two trains to pass one another is 12 seconds.

Hence, option (d).

Workspace:

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