Question 1

Two trains running in opposite directions cross a man standing on the platform 54s and 34s respectively and they cross each other in 46 s . Find the ratio of their speeds.?

Accepted Answer

Let the speeds of two trains be x and y, respectively . ∴ Length of 1st train = 54x Length of the 2nd train = 34y According to the question. (54x + 34y) / (x + y) = 46 ⇒ 54x + 34y = 46x + 46y ⇒ 27x + 17y = 23x + 23y ⇒ 4x = 6y ⇒ x/y = 3/2 ∴ x : y = 3 : 2

Question 2

Two trains are running 40 km/h and 20 km/h respectively, in the same directions. The fast train completely passes a man sitting in the slow train in 5 s. The length of the fast a train is?

Accepted Answer

The length of the fast train = Relative speed x Time = (40 - 20) x (5/18) x 5 = 277/9 m

Question 3

Two trains of same length take 6 s and 9 s, respectively to cross a pole. If both the trains are running in the same direction, then how long will they take to cross each other?

Accepted Answer

Given that, t1 = 6 s and t2 = 9 s Then, time taken by the trains to cross each other = 2t1 t2 / (t2 - t1) = (2 x 6 x 9)/(9 - 6) = 36 s

Question 4

P and Q are 27 km away. Two trains will having speeds of 24 km/h and 18 km/h respectively starts simultaneously from P and Q and travel in the same direction. They meet at a point R beyond Q. Distance QR is

Accepted Answer

If the trains meet after t h. Relative speed of train = (24 -18) = 6 km/h ⇒ Distance = 27 ∴ t = 27/6 = 9/2 h ∴ QR distance travel by train which is travelling at a speed of 18 km/h = 18t = 18 x 9/2 = 81 km

Question 5

Two station P and Q are at a distance of 160 km. Two trains starts moving from P and Q to Q and P respectively and meet each other after 4 h . If speed of the train starting from P is more than that of other train by 6 km/h. then find the speeds of …

Accepted Answer

Let the speed of both trains be V km/h and (V + 6) km/h, respectively Then, according to the question. 160 = V x 4 + (V + 6) x 4 ⇒ 160 = 4V + 4V + 24 ⇒ 40 = V + V + 6 ⇒ 2V + 6 = 40 ⇒ 2V = 34 ∴ V = 17 Hence, speeds of both the trains are 17 km/h and (17 + 6 ) km/h i,e 17 km/h and 23 km/h .

Question 6

A train leaves Mumbai for Goa at 3:45 pm and goes at the rate of 50 km/h. Another train leaves Goa for Mumbai at 2:35 pm and distance between Mumbai and Goa is 510 km. at what distance from Mumbai will the two trains meet?

Accepted Answer

Let the two trains meet at D km from Mumbai. Then, 3:45 pm + D/50 = 2 : 35 pm + 510 - D/60 ⇒ (3:45 pm - 2:35 pm) + (D/50 + D/ 60) = 510/60 ⇒ (11/6 h) + D{( 50 + 60 / 50 x 60)} = 17/2 ⇒ D(110/3000) = 17/2 - 7/6 ⇒ D(110/3000) = (51 - 7)/6 = 44/6 ∴ D = (44/6) x (3000/110) = 200 km

Question 7

Train A crosses a pole in 25 s and train B crosses the pole in 1 min 15 s . Length of train A is half the length of train B. What is the ratio between the speeds of A and B, respectively?

Accepted Answer

Let the lengths of the trains A and B be a and 2a, respectively. when a train crosses a pole, it covers the distance equal to its length. ∴ Required ratio of speeds = a / 25 : 2a /75 = 3 : 2

Question 8

A 110 m long train crosses a tree in 3 s. How long will take to cross 165 m long platform and 135 m long bridge, if platform and bridge are at a distance of 30 m?

Accepted Answer

The distance covered by the train to cross the platform and bridge = Length of the platform + Length of bridge + Distance between platform and bridge + Length of the train = 165 + 135 + 30 + 110 = 440 m Speed of train = 110 /3 m/s ∴ Required time taken = 440/(110/3) = 12 s

Question 9

The distance travelled by a train is 1830 km. The speed of the train is one more than twice the time taken to travel the distance. What will be the respective ratio of the speed of the train and time taken to travel?

Accepted Answer

Let time taken to cover the distance = t ∴ Speed = (2t + 1) ⇒ t(2t + 1) = 1830 ⇒ 2t2 + t = 1830 ⇒ 2t2 + t - 1830 = 0 ∴ t = -1 ± √(1)2 - 4 x 2 x(-1830) / 2 x 2 = -1 ± √1 + 14640 / 4 = -1 ± 121 / 4 Taking '+' sign t = -1 + 121 / 4 = 120/4 = 30 ∴ Required ratio = (2 x 30 + 1) : 30 = 61 : 30

Question 10

The average speed of a bus is three-fourth the average speed of a train. The train covers 240 km in 12 h . How much distance will the bus cover in 7 h?

Accepted Answer

Average speed of train = 240/12 = 20 km/h Average speed of bus = (3/4) x 20 = 3 x 5 = 15 km/h Required distance = 15 x 7 = 15 km/h

Question 11

The distance between two stations P and Q is 145 km. A train with speed of 25 km/h leaves station at 8 : 00 am towards station Q. Another train with speed of 35 km/h leaves station Q at 9:00 am towards station P. Then, at what time both trains meet?

Accepted Answer

First train leaves at 8 :00 am and second at 9:00 am. So, first train i,e from P to Q has covered 25 km distance in 1 h. So, distance left between the station = 145 - 25 = 120 km Now, trains are travelling in opposite directions, So, relative speed = 25 + 35 = 60 km/h Time taken to cover 120 km = 120/60 = 2h ∴ The time, at which both the trains will meet, is 2 h after second train left i.e., 9 : 00 am + 2h = 11 : 00 am

Question 12

A train, 500 m long passes a standing train in 20 s moving at a speed of 100 km/h. Find the length of the standing train?

Accepted Answer

Let x be the length of the standing train ∴ Speed of the train = (500 + x)/20 ⇒ 100 x (5/18) = (500 + x)/20 ⇒ 500 + x = (100 x 5 x 20)/18 ⇒ 500 + x = 555.56 ∴ x = 555.56 - 500 = 55.56 m

Question 13

Two trains travel in opposite direction at 32 km/h and 40 km/h and a man sitting in slower train passes the faster train in 6 s. The length of the faster train is?

Accepted Answer

Relative speed = (32 + 40) = 72 km/h = (72 x 5/18) m/s = 20 m/s ∴ Length of train = (20 x 6) = 120 m

Question 14

Two trains 121 m long and 99 m long are running in opposite direction, first at 40 km/h and the second at 32 km/h. In what time will they completely clear off each other from the moment they meet?

Accepted Answer

Total distance to be traveled = 121 + 99 = 220 m Relative speed = Sum of speeds = 72 km/h = 72 x (5/18) = 20 m/s ∴ Required time = 220/20 = 11s

Question 15

A train travailing at a speed of 30 m/s crosses a 600 m long platform in 30 s. Find the length of the train.

Accepted Answer

Let length of the train be x m. Relative length of the train = (x + 600) m According to the question, (x + 600)/30 = 30 ⇒ x + 600 = 900 ∴ x = 900 - 600 = 300 m

Question 16

A train passes two persons two persons who are walking in the direction opposite to the direction of train at the rate of 10 m/s and 20 m/s respectively in 12 s and 10 s, respectively. Find the length of the train?

Accepted Answer

Let the speed of the train be V According to the question. (V + 10) x 12 = (V + 20) x 10 ⇒ 6V + 60 = 5V + 100 ⇒ x = 100 - 60 = 40 m/s ∴ Length of the train = (V + 10) x 12 = (40 + 10) x 12 = 600 m

Question 17

Two train are running in opposite direction with a speed of 62 kmph and 40 kmph respectively. If the length of one train is 250 meters and they cross each other in 18 seconds, the length of the other train is?

Accepted Answer

Let the length of another train be L meters. Their relative speed = (62 + 40) km/hr = 102 x (5/18) = (85/3) m/sec ∵ 250 + L/(85/3) = 18 ⇒ 3(250 + L)/85 = 18 ⇒ 250 + L = 510 ⇒ L = 260 ∴ Length of another train = 260 meters

Question 18

A train travels 100 meters at 70 km hour. A man is running at 10 km per hour in the same direction. What time the train will pass the man?

Accepted Answer

Relative speed of the train = (70 - 10) = 60 km/hr = (60 x 5/18) = 50/3) m/sec. ∴ Time taken by the train to pass the man = (100 x 3/50) = 6 sec.

Question 19

A train 120 meters long is running at a rate of 54 km/hr. Time taken by the train to cross a tunnel 130 meters long is?

Accepted Answer

∵ Speed of the train = 54 x (5/18) m/sec = 15 m/sec ∴ Time taken by the train to cross the tunnel = Time taken by it to cover (120 + 130) m = (250/15) sec = 162/3

Question 20

Two trains are running on parallel lines in the same direction at a speed of 50 km and 30 km per hour respectively. The faster train crosses a man in slower train in 18 seconds. The length of the faster train is?

Accepted Answer

Relative speed of both trains = (50 - 30) = 20 km/hr = 20 x (5/18) m/sec. = (50/9) m/sec. Let the length of the faster train be L Then, (L x 9)/50 = 18 ⇒ L = (18 x 50)/9 = 100 meters

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