Problems on Trains
- 1. Two trains A and B start from Delhi and Patna toward Patna and Delhi, respectively. After passing each other, they take 16 h and 9 h to reach Patna and Delhi, respectively. If the train from Delhi is moving at 90 km/h, then find the speed of the other train (in km/h) .?
Options- A. 120
- B. 190
- C. 125
- D. 145 Discuss
Correct Answer: 120
Explanation:
Given t1 = 16 h , t2 = 9 h and a = 90 km/h
According to the question
? Speed of B = a?t1/ t2
= 90 x ?16/9
= 90 x 4/3
= 30 x 4 = 120 km/h
- 2. A train takes 9 s to cross a pole. If the speed of the train is 48 km/h, then length of the train is?
Options- A. 150 m
- B. 120 m
- C. 90 m
- D. 80 m Discuss
Correct Answer: 120 m
Explanation:
Let the length of the train be L m.
New , speed = 48 km/h = 48 x (5/18) m/s
Train takes 9 s to cross a pole.
? : Length of train, L = Speed x Time
= 48 x (5/18) x 9 = 120 m
- 3. A train running at the speed of 72 km/h goes past a pole in 15 s. What is the length of the train?
Options- A. 150 m
- B. 200 m
- C. 300 m
- D. 350 m Discuss
Correct Answer: 300 m
Explanation:
Speed of train = Length of train / Time taken to cross the stationary object
? Length of train = Speed of train x Time taken to cross the stationary object
= 72 x 5 x (15/18) = 300 m
- 4. 150 m long train running with the speed of 90 km/h to cross a bridge in 26 s .What is the length of the bridge?
Options- A. 500 m
- B. 600 m
- C. 659 m
- D. 550 m Discuss
Correct Answer: 500 m
Explanation:
Let length of bridge be L m.
We know, Speed = Distance/Time
According to the question,
90 x 5/18 = 150 + L/26
? 25 x 26 = 150 + L
? 650 = 150 + L
? L = 500 m
- 5. A train crosses a platform in 30 s travelling with a speed of 60 km/h. If the length of the train be 200 m, then the length of the platform is?
Options- A. 420 m
- B. 500 m
- C. 300 m
- D. 250 m Discuss
Correct Answer: 300 m
Explanation:
Speed of train = 60 km/h = 60 x (5/18) m/s = 50/3 m/s
Let length of the platform be L m.
According to the question,
200 + L = (50/3) x 30
? 200 + L = 500
? L = 300 m
- 6. A train crosses a bridge of length 150 m in 15 s and a man standing on it in 9 s. The train is travelling at a uniform speed. Length of the train is?
Options- A. 225 m
- B. 200 m
- C. 135 m
- D. 90 m Discuss
Correct Answer: 225 m
Explanation:
Let the length of the train be L m.
According to the question,
L/9 = Speed ...(i)
and (L + 150)/15 = Speed ..(ii)
from Eqs. (i) and (ii) we get
L/9 = (L + 150)/15
? L/3 = (L + 150)/5
? 5L = 3L + 450
? L = 225 m
- 7. A train moving with uniform speed crosses a pole in 2 s and a 250 m long bridge in 7 s. Find the length of the train?
Options- A. 150 m
- B. 120 m
- C. 100 m
- D. 80 m Discuss
Correct Answer: 100 m
Explanation:
Let length of the train be L m.
According to the question,
L/2 = (L + 250)/7
? 7L = 2L + 500
? 7L - 2L = 500
? 5L = 500
? L = 500/5 = 100 m
- 8. The lengths of a train and a platform are equal. If a train running at a speed of 90 km/h, crossed the platform in 1min, then find the length of the train.?
Options- A. 500 m
- B. 550 m
- C. 600 m
- D. 750 m Discuss
Correct Answer: 750 m
Explanation:
Let length of both train and platform be L.
Distance covered by the train to cross the platform = L + L = 2L
Time =1 min = 60 s
and speed = 90 km/h = 90 x 5/18 = 25 m/s
? Distance = Speed x Time
? 2L = 25 x 60
? L = 750 m
- 9. A train travelling with uniform speed crosses two bridges of lengths 300 m and 240 m in 21 s and 18 s respectively. Find the speed of the train?
Options- A. 72 km/h
- B. 68 km/h
- C. 65 km/h
- D. 60 km/h Discuss
Correct Answer: 72 km/h
Explanation:
Let length of the train = L
According to the question,
(L + 300)/21 = (L + 240)/18
? (L + 300)/7 = (L + 240)/6
? 6L + 1800 = 7L + 1680
? L = 120 m
Taking the length of the 2nd bridge into consideration,
Speed of train = (L+ 240)/18 = (120 + 240)/18 m/s
= (360/18) x (18/5) km/h
= 72 km/h
- 10. Two train of length 70 m and 90 m are moving in opposite directions at 10 m/s and 6 m/s, respectively. Find the time taken by trains to cross each other .?
Options- A. 10 s
- B. 8 s
- C. 12 s
- D. 16 s Discuss
Correct Answer: 10 s
Explanation:
According to the formula .
Required time = (x + y) / (u + v)
Here, x = 70 m, y = 90 m, u = 10 m/s and v = 6 m/s
? Required time = (70 + 90) / (10 + 6) = 160/16 = 10 s
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