Question 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 oth…

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 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.?

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 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 .?

Accepted Answer

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

Question 11

A 400 m long train takes 36 s to cross a man walking at 20 km/h in the direction opposite to that of the train. What is the speed of the train?

Accepted Answer

Relative speed of train = 400/36 m/s = 400/36 x (18/5) = 40 km/h Relative speed of train = Speed of train + Speed of man ⇒ 40 = Speed of train + 20 ∴ Speed of train = 40 - 20 = 20 km/h

Question 12

Two trains of lengths 105 m and 90 m, respectively run at the speeds of 45 km/h and 72 km/h, respectively in opposite directions on parallel tracks. Find the time which they take to cross each other?

Accepted Answer

Total length of the train = 105 + 90 = 195 m Relative speed = 72 + 45 km/h = 117 km/h = 117 x (5/18) = 585/18 m/s ∴ Required time = (195 x (18/585) s = 6 s

Question 13

A 110 m long train is running at a speed of 60 km/h. How many seconds, does it take to cross an another train of length 170 m, which is standing on parallel track?

Accepted Answer

Speed = 60 km/h = 60 x (5/18) m/s = 50/3 m/s Required time = (110 + 170) / (50/3) = (280 x 3)/50 = 16.8 s

Question 14

Two train of equal length are running on parallel lines in the same direction at 46 km/h and 36 km/h. The faster train passes the slower train in 36 s. The length of each trains is?

Accepted Answer

Let the length of each train be L m. Relative speed = 46 - 36 = 10 km/h = 10 x 5/18 m/s = 25/9 m/s Sum of length of train / Relative speed of train = Time taken ∴ 2L/(25/9) = 36 ⇒ 2L = (36 x 25)/9 = 100 ∴ L = 50 m.

Question 15

Two trains of same length are running in parallel tracks in opposite directions with speeds 65 km/h and 85 km/h respectively. They cross each other in 6 s . The length of each train is?

Accepted Answer

Let length of each train be L m. Then. (65 + 85 ) x 5/18 = (L + L)/6 ⇒ (150 x 5 x 6)/18 = 2L ⇒ 2L = 250 ∴ L = 125 m

Question 16

Two train start at the same time from points x and y towards each other and after crossing, they take 9 h and 4 h in reaching points y and x, respectively. Find the ratio of speeds of the 1st train to that of the 2nd train?

Accepted Answer

Given that, T1 = 9 h and T 2 = 4 h According to the formula. (1st train's speed) : (2nd train's speed) = √4 : √9 = 2 : 3

Question 17

The ratio between the speeds of two train is 8 : 9 Second train covers 360 km in 4 h. Distance covered by first train in 3 h (in km ) is?

Accepted Answer

Let speed of 1st train be 8S and speed of 2nd train be 9S According to the question. Speed of second train = 360/4 = 90 km/h 9S = 90 ⇒ S = 10 So, speed of 1st train = 8 x 10 = 80 km/h ∴ Required distance = 80 x 3 = 240 km

Question 18

From station M and N, two trains start moving towards each other at speed 125 km/h and 75 km/h, respectively. When the two trains meet each other, it is founds that one train covers 50 km more than another. Find the distance between M and N.?

Accepted Answer

Let the trains meet after time t at a distance x from station N. Then another train coming from station M covers a distance of (x + 50) For station M, (x + 50) = 125t ⇒ x = 125t - 50 ..(i) For station N, x = 75t .....(ii) From Eqs. (i) and (ii), we get 75t = 125t - 50 ⇒ t = 1h Distance between station M and N = 125 + 75t = 200 x 1 = 200 km

Question 19

Excluding stoppages, the speed of a train is 108 km/h and including stoppages, it is 90 km/h. For how many minute does the train stop per hour?

Accepted Answer

Because of stoppages, train covers 18 km less per hour . ∴ Time taken to cover 18 km = 18/108 = 1/6 h = (1/6) x 60 = 10 min

Question 20

Without stoppages, the speed of a train is 150 km/h and with stoppages, it is 100 km/h. How many minutes does the train stop?

Accepted Answer

Because of stoppages, train covers 50 km less per hour. ∴ Time taken taken to cover 50 km = 50/150 h = (50/150) x 60 = 20 min

Problems on Trains Questions