வெல்லுங்கள் CSAT 2025 - 12: Q and A - Problems on Trains

Questions & Answers (Multiple Choice) - TRAIN PROBLEMS
கொள்குறி வினா- விடைகள் - புகைவண்டி-கணக்குகள்

1. The ratio between the speeds of two trains is 3 : 5. If the second train runs 420 kms in 4 hours, then what is the speed of the first train?
a. 105kmph b. 63kmph
c. 52.5kmph d. 72kmph

2. A train 120m long is running at 72kmph. In how much time will it pass a platform 360m long?
a. 48 sec b. 32 sec
c. 24 sec d. 42 sec

3. A train P leaves City A at 9 a.m and reaches City B at 1 p.m. Another train Q leaves City B at 8 a.m and reaches City A at 11.30 a.m. At what time do the 2 trains cross one another?
a. 10.20 a.m b. 10.00 a.m
c. 10.30 a m d. 10.10 a.m

4. A train covers a distance in 40 minutes, if it runs at a speed of 48kmph on an average. What will be the speed to be added at which the train must run to reduce the time of journey to 30 minutes?
a. 64 kmph b. 36 kmph
c. 32.5 kmph d. 16 kmph

5. Two trains running in opposite directions cross a man standing on the platform in 12 seconds and 19 seconds respectively and they cross each other in 15 seconds. The ratio of their speeds is
a. 4 : 5 b. 4 : 3
c. 5 : 4 d. 3 : 2

6. A bullet train crosses a man standing on the platform 350m long in 16 sec and crosses the platform completely in
23 sec. The speed of the train is
a. 120 kmph b. 160kmph
c. 180 kmph d.140 kmph

7. A train running at 72kmph takes 24 seconds to pass compltely a platform. Next it takes 6 seconds to pass a man running at the rate of 12kmph in the same direction. Find the length of the platform.
a. 380m b. 480m
c. 100m d. 280m

8. Two trains travel in the same direction at the speed of 76kmph and 49kmph. The faster train passes a man sitting in the slower train in 32 seconds. The length of the faster train is
a. 360m b. 480m
c. 120m d. 240m

9. Two stations P and Q are 240km apart. A train starts from P at 7.00a.m towards Q at 56 kmph. Another train starts from Q at 8.00a.m towards P at 36 kmph. When the two trains will cross each other?
a. 10.20 a.m b. 10.00 a.m
c. 11.00 a m d. 10.40 a.m

10. A train can travel 50% faster than a car. Both start from the point A and reach the point B at the same time. B is 150km apart from A. On the way, however the train lost 25 minutes while stopping at stations. The speed of the car is
a. 160kmph b. 180kmph
c. 120kmph d. 140kmph

11. Two trains 120m long, moving in opposite directions, cross each other in 10 seconds. If one is moving twice as fast as the other, then the speed of the slower train is
a. 28.8kmph b. 30kmph
c. 32kmph d. 57.6kmph

12. A train 260m long is running at a speed of 70kmph. In what time will it pass a man who is running at 8kmph in the direction opposite to that of train which is going?
a. 18 sec b. 20 sec
c. 6sec d. 12 sec

13. A train crossed an electric pole in 20 seconds and a platform of length 250m long completely in 45 seconds. The length of the train is
a. 160m b. 200m
c. 220m d. 240m

14. A train travelling at 78kmph completely crosses another train having twice its length and travelling in opposite direction at 66kmph in 12 seconds. The length of the longest train is
a. 160m b. 480m
c. 320m d. 240m

15. A train overtakes two persons who are walking in the same direction of which the train is going, at the rates of
2kmph and 4kmph and passes them in 9 and 10 seconds respectively. The length of the train is
a. 50m b. 80m
c. 100m d. 60m

Answers

1. b 2. c 3. a 4. d 5. b

6. c 7. a 8. d 9. b 10. c

11. a 12. d 13. b 14. c 15. a

Explanation to Answers

1. The speed of the second train
= 420/4 = 105 kmph

The speed of the first train
= (3/5)×105 = 63 kmph

2. 1 kmph => (5/18) m/sec
To pass a platform 360m long by 120m long train @ 72kmph, the time taken
72 × (5/18) × t = (120+360)
=> 20t = 480 => t = 24seconds.

3. Let the soeeds of P and Q be x kmph and y kmph respectively.
4x = 3.5 y -> 8x = 7y -> y = (8/7)x
Distance between two stations A and B is 4x.
At 9.00a.m the train Q traveled
(8/7)x km. Now the distance between Pand Q is 4x - (8/7)x = (20/7)x
Relative speed x + (8/7)x = (15/7)x
Time taken to cross each other
{4x - (8/7)x}/{ (15/7)x}
= 20/15 = 4/3 hours.
At 10.20 , they cross each other.

4. The distance covered at a speed of
48 kmph in 40 minutes
= 48×(40/60) = 32 km
Since the diatance 32km covered in 30 minutes, the speed of the train would be
= (32/30)×60 = 64 kmph.
The speed to be added
= 64 - 48 =16kmph

5. Let the speeds of two trians be p m/sec and q m/sec respectively.
Lengths of the trains 12p and 19q.
So (12p + 19q)/(p+q) = 15
-> 12p + 19q = 15 (p+q)
-> 19q -15q = 15p - 12p
-> 4q = 3p
-> p/q = 4/3
Ratio is 4 : 3

6. 350m =Length of platform
= distance covered by the train in (23 - 16 = 7) seconds.
Speed of the train
= (350/7) × (18/5)
= 180kmph.

7. Length of the train + lengrh of the platform = 72 ×(5/18)×24 = 480m.
Since the train passes a man running at the rate of 12kmph in the same direction,
The relative speed = 72 - 12 = 60kmph.
Length of the train = distance covered in 6 seconds at the speed of 60kmph
= 60 ×(5/18)×6 = 100m.
So, Length of platform
= 480 - 100 = 380m.

8. Relative speed = 76 - 49 = 27kmph
Length of the faster train
= 27 × (5/18) × 32 = 240m.

9. At 8.00a.m the train starts from P at 7.00a.m covered 56km.
The remining distance to be covered by both the trains with relative speed 92km
(56+36)
i e., (240 - 56)/(92) = 184/92 = 2 hrs.
Hence at 10.00a.m, the two trains will cross each other.

10. Let the speed of the car be 's' kmph.
So the speed of the train is (3/2)s.
By problem,
(150/s) - (150)/{(3/2)s} = 25/60
-> 150/s - 100/s = 25/60
-> 50/s = 25/60 -> s = 120kmph

11. Let the speed of the slower train be
's' metres/sec.
So the speed of the faster train is
'2s' metres/sec.
Relative speed = s + 2s = 3s
Here (120 + 120)/10 = 3s
-> s = 8m/sec
-> speed in kmph = 8×(18/5) = 28.8

12. Relative speed = 70 + 8 = 78kmph
-> 78×(5/18) = (65/3)m/sec
Time taken by the train to pass the man
= (260)/(65/3) = 12 sec.

13. The distance covered in
(45 - 20) seconds = 250m
In 25 seconds the distance covered is 250m.
The length of the train is = the distance covered in 20 seconds = (250/25)×20
= 200m

14. Let the length of the first train be
'l' metres.
So the length of the other train is
'2l' metres.
Relative speed = 78+ 66 = 144kmph
Relative speed in metres per second
= 144×(5/18) = 40m/sec
So l + 2l = 40×12 =480
-> l = 160m
Hence the length of the longest train is
2×160 = 320m

15. Let the speed of the train be 's' kmph and the length of the train be 'l' metres.
Here
l = (s-2)×(5/18)×9 = (s-4)×(5/18)×10
-> 9s - 18 = 10s - 40
-> s = 22
Hence l = (22-2)×(5/18)×9 = 50m.

- கட்டுரையாளர், போட்டித் தேர்வு பயிற்சியாளர், குளோபல் விக்கிமாஸ்டர்; தொடர்புக்கு: success.gg@gmail.com

முந்தைய அத்தியாயம் > வெல்லுங்கள் CSAT 2025 - 11: Q and A on Time & Work