# Important Formulas

# Problems on Trains

Q1. A train moves with the speed of 180 km/hr. Find the
speed in m/sec ?

(a) 20 m/sec

(b) 30 m/sec

(c) 50 m/sec

(d) 70 m/sec

**Answer:** (c) 50 m/sec

180 km/hr = 180 X (5/18) = 50 m/sec

Q2. A 150 metres long train moving at the speed of 126
km/hr. What time it will take to cross an electric pole ?

(a) 3.5 seconds

(b) 4.2 seconds

(c) 5 seconds

(d) 6 seconds

**Answer:** (b) 4.2 seconds

126 km/hr = 126 X (5/18) = 35 m/sec

So the time taken by the train = (150/35) = 4.2 sec

Q3. A train of length 250 meter long running at the speed
of 10 m/sec. How much time it will take to cross a platform
of 650 meter length ?

(a) 60 seconds

(b) 72 seconds

(c) 85 seconds

(d) 90 seconds

**Answer:** (d) 90 seconds

Total length to cross the platform = 250 + 650 = 900 meter

So the time taken by the train = (900/10) = 90 sec

Q4. A train with a uniform speed crosses a pole in 2
seconds and a bridge of length 250m in 7 seconds. The length
of the train is ?

(a) 85 metre

(b) 100 metre

(c) 105 metre

(d) 125 metre

**Answer:** (b) 100 metre

Let the length of the train is x metre

Speed of the train is,

x/2 = (x + 250)/7

7x = 2x + 500

x = 100 metre

Q5. A train of 260 m long passed a pole in 26 secconds.
How long will it take to pass a platform of 740 m long ?

(a) 78 seconds

(b) 96 seconds

(c) 100 seconds

(d) 115 seconds

**Answer:** (c) 100 seconds

Speed of the train = 260/26 = 10 m /sec

So required time to cross the platform is,

=(260 + 740 )/10

=100 sec

Q6. A train travels first 160 Km at 64 Km/hr and the next 160 Km at 80 Km/hr. The average speed for the first 320 Km of the tour is

(a) 57.24 km/hr

(b) 71.11 km/hr

(c) 78.32 km/hr

(d) 91 km/hr

**Answer:** (b) 71.11 km/hr

Total time taken =( (160/64) + (160/80)) hrs= 9/2 hrs

Average Speed

=(320 X (2/9)) km/hr

=71.11 km/hr

Q7. The ratio between the speeds of two trains is 5 : 6. If the second train runs 600 km in 5 hours, the speed of the first train is

(a) 30 km/hr

(b) 90 km/hr

(c) 100 km/hr

(d) 300 km/hr

**Answer:** (c) 100 km/hr

Let the speed of the first train is 5x km/hr

Let the speed of the 2nd train is 6x km/hr

Now speed of 2nd train = 600/5 km/hr = 120 km/hr

A/Q 6x = 120

=> x = 20

∴ Speed of the 1st train = 5 X 20 = 100 km/hr

Q8. Two trains approach each other at 30 km/hr and 27 km/hr from two places 342 km apart. After how many hours will they meet ?

(a) 6 hrs

(b) 9 hrs

(c) 10 hrs

(d) 11 hrs

**Answer:** (a) 6 hrs

Let the two trains meet after x hours

A/Q 30x + 27x = 342

=> 57x = 342

=> x = 342/57 = 6

∴ Both the train will meet after 6 hours

Q9. The speed of a 180m long train is 60 km/hr. How much time will take to pass a platform of 600m long ?

(a) 40 sec

(b) 42.5 sec

(c) 45.8 sec

(d) 46.8 sec

**Answer:** (d) 46.8 sec

Speed = 60 km/hr = (6000 / (60X60)) m/sec = 50/3 m/sec

Required time = | Distance | = | 600 + 180 | sec | = | 780 X 3 | sec |

Speed | 50/3 | 50 |

= 46.8 sec

Q10. A train travelling at a speed of 30 m/sec crosses a platform 600m long in 30 seconds. The length of the train is

(a) 200m

(b) 250m

(c) 300m

(d) 450m

**Answer:** (c) 300m

Let the length of the train be x meter

∴ Speed of the train = (600+x)/30 m/sec

=> 30 m/sec = (600+x)/30 m/sec

=> 600 + x = 900

=> x = 900 - 600 = 300m