Problems on Trains
Q11. A 230m long train crosses a bridge in 30 seconds at 45 km/hr. The length of the bridge is
(a) 130m
(b) 145m
(c) 245m
(d) 250m
Answer: (b) 145m
Let the length of the bridge be x meter
| Now speed = | 230 + x | m/sec |
| 30 |
| => 45 km/hr = | 230 + x | m/sec |
| 30 |
| => | 45 X 1000 | m/sec = | 230 + x | m/sec |
| 60 X 60 | 30 |
| => | 25 | = | 230 + x |
| 2 | 30 |
=> 460 + 2x = 750
=> 2x = 750 - 460
=> x = 290/2 = 145 m
Q12. A train crosses a pole in 15 seconds, while it crosses a 100m long platform in 25 seconds. The length of the train is
(a) 125m
(b) 135m
(c) 150m
(d) 200m
Answer: (c) 150m
Let the length of the train be x meter
Now x/15 = (100+x)/25 => 25x = 1500 + 15x
=> 10x = 1500
=> x = 150m
Q13. A fast train takes 3 hours less than the slow train for a journey of 600 km. If the speed of the slow train is 10 km/hr less than the fast train, the speed of the slow train is
(a) 32 km/hr
(b) 40 km/hr
(c) 46 km/hr
(d) 51 km/hr
Answer: (b) 40 km/hr
Let the speed of the slow train is x km/hr
∴ the speed of the fast train is (x + 10) km/hr
| Fast train takes the time = | 600 km | = | 600 | hr |
| (x + 10) km/hr | x + 10 |
| Slow train takes the time = | 600 km | = | 600 | hr |
| x km/hr | x |
| A/Q | 600 | = | 600 | - 3 |
| x + 10 | x |
| ⇒ | 600 | = | 600 - 3x |
| x + 10 | x |
⇒ 600x = (600 - 3x)(x + 10)
⇒ 600x = 600x + 6000 - 3x2 - 30x
⇒ 3x2 + 30x - 6000 = 0
⇒ x2 + 10x - 2000 = 0
⇒ x2 + 50x - 40x - 2000 = 0
⇒ x(x + 50) - 40(x + 50) = 0
⇒ (x - 40)(x + 50) = 0
∴ x - 40 = 0
⇒ x = 40 km/hr
Q14. Two trains starts from two stations A and B and travel towards each other at 40 km/hr and 50 km/hr respectively. At the time of their meeting, the second train has travelled 110 km more than the first. The distance between A and B is
(a) 850 Km
(b) 870 Km
(c) 935 Km
(d) 990 Km
Answer: (d) 990 Km
Let, the two trains meet after x hours
Now 50x = 40x + 110
⇒ 50x - 40x = 110
⇒ 10x = 110
⇒ x = 11
∴ Distance between A and B = (40 X 11 + 50 X 11) Km = (440 + 550) Km = 990 Km
Q15. A train covered a certain distance at a uniform speed. If the train had been 5 km/hr faster, it would have taken 3 hours less than the schedule time. If the train were slower by 5 km/hr, the train would have taken 5 hours more than the schedule time. The length of journey is
(a) 120 Km
(b) 140 Km
(c) 160 Km
(d) 180 Km
Answer: (d) 180 Km
Let the required distance be x km and uniform speed be y km/hr
| Now | x | - | x | = 3 --------(1) |
| y | y + 5 |
| Now | x | - | x | = 5 --------(2) |
| y - 5 | y |
| (1) ⇒ | x(y + 5) - xy | = 3 |
| y(y + 5) |
⇒ xy + 5x - xy = 3y2 + 15y
⇒ 3y2 + 15y = 5x ------ (3)
| (2) ⇒ | xy - x(y - 5) | = 5 |
| y(y - 5) |
⇒ xy - xy + 5x = 5y2 - 25y
⇒ 5y2 - 25y = 5x ------ (4)
From (1) and (4) ⇒ 3y2 + 15y = 5y2 - 25y
⇒ 2y2 = 40y
⇒ y = 20
(3) ⇒ 3 X 202 + 15 X 20 = 5x
⇒ 1200 + 300 = 5x
⇒ 5x = 900
⇒ x = 180 km
Q16. Bombay Express left Delhi for Bombay at 14.30 hours travelling at a speed of 70 km/hr and Rajdhani Express left Delhi for Bombay on the same day at 15.30 hours travelling at a speed of 90 km/hr. How far away from Delhi will the two trains meet ?
(a) 285 Km
(b) 290 Km
(c) 315 Km
(d) 345 Km
Answer: (c) 315 Km
Let, the trains meet at a distance of x km from Delhi.
| Then | x | - | x | = 1 |
| 70 | 90 |
| ⇒ | 9x - 7x | = 1 |
| 630 |
⇒ 2x = 630
⇒ x = 315 km
Q17. A train without stoppages travels at the rate of 60 km/hr and with stopagges it travels at 55 km/hr. How many minutes does the train stop on an average per hour ?
(a) 5 min
(b) 8 min
(c) 10 min
(d) 12 min
Answer: (a) 5 min
Due to stoppages it covers 5 Km less per hour
Required Time taken to cover 5 km = (5/60) X 60 min = 5 min
Q18. A train travelled distances of 10 km, 20 km and 30 km at speeds of 50 km/hr, 60 km/hr and 90 km/hr respectively. The average speed of the train was
(a) 67.25 km/hr
(b) 69.23 km/hr
(c) 70.12 km/hr
(d) 72.45 km/hr
Answer: (b) 69.23 km/hr
Total distance covered = 10 km + 20 km + 30 km = 60 km
| Total Time taken = ( | 10 | + | 20 | + | 30 | ) hr |
| 50 | 60 | 90 |
| = ( | 1 | + | 1 | + | 1 | ) hr |
| 5 | 3 | 3 |
| = | 3 + 5 + 5 | h = | 13 | h |
| 15 | 15 |
| Average Speed = | 60 | km/hr = | 60 X 15 | km/hr = | 900 | km/hr = 69.23 km/hr |
| 13/15 | 13 | 13 |
Q19. Two trains A and B start running together from the same point in the same directions at 50 km/hr and 60 km/hr respectively. If the length of each train is 200 m, how long will it take for the train B to cross train A.
(a) 121 Sec
(b) 135 Sec
(c) 144 Sec
(d) 156 Sec
Answer: (c) 144 Sec
| Relative Speed = (60 - 50) km/hr = 10 km/hr = | 10 X 1000 m | = | 100 | m/Sec = | 25 | m/Sec |
| 60 X 60 Sec | 36 | 9 |
Total Distance covered = 200 + 200 = 400 m
∴ Required time = 400 X (9/25) Sec = 16 X 9 Sec = 144 Sec
Q20. A train 200 m in length passes a milestone in 20 Sec and another train of the same length travelling in opposite direction in 15 Sec. The speed of the second train is
(a) 12 1/3 m/sec
(b) 15 2/5 m/sec
(c) 16 2/3 m/sec
(d) 18 3/5 m/sec
Answer: (c) 16 2/3 m/sec
Speed of the first train = 200/20 m/sec = 10 m/sec
Let the speed of the second train be x m/sec
Relative Speed = (10 + x) m/sec
Total distance = 200 + 200 = 400 m
| A/Q | 400 | = 15 |
| 10 + x |
⇒ 400 = 15 (10 + x)
⇒ 400 = 150 + 15x
⇒ 15x = 250
⇒ x = 250/15 = 50/3 = 16 2/3 m/sec
Practice Test Exam