Preparations for IPM, MTSE, Olympiad, MAT, Scholarship,CBSE, ICSE & Board Math Exam

Tuesday, December 24, 2013

Wednesday, November 27, 2013

train

Problems on train

1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

Answer:

Speed of train = 60 Km/h = 60 x 5/18 = 50/3 m/s

Time taken to cross the pole = 9 secs

So, length of the train = speed x time = (50/3) x 9 = 150 m

2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

Answer:

Since the man is running in the same direction of the train the relative speed will be (St – 5)

Time taken to cross =0. 125 / (St – 25/18) = 10/3600

Or, St – 5 = (0.125 x 3600/10) = 45

Or, St = (45 + 5) = 50 km/hr

3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is -------------------

Answer:

Total length the train has to cross = 130 + Lb

Where Lb = length of the bridge

130 + Lb = 45 x (5/18) m/s x 30 s = 25 x 15

Lb = 245 m

	4. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is ----------------------- Answer: Let the speed of the two trains be A and B Length of the trains are La and Lb Now, La = 27A, Lb = 17B (La + Lb) = 23(A + B) Therefore, 27A + 17B = 23(A + B) Or, 4A = 6B Or, A/B = 3/2

	5. Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is

Let the total distance be x between Howrah to Patna. Let the two trains meet at distance y from Howrah. Let speed of the trains be Va and Vb km/hr respectively.

Since they start simultaneously, the time taken to meet will be same.

So, time taken to meet = (y/Va) = (x – y)/Vb

Or, yVb = (x – y)Va --------------- (1)

Also the time taken for remaining journey is given,

Therefore, 16 = y/Vb and 9 = (x – y)/Va

Or, y = 16Vb and x – y = 9Va ----- (2)

Substituting 2 in 1, we get

16Vb .Vb = 9Va.Va

Or, 4Vb = 3Va -------- taking square root

Or, Va/Vb = 4/3

	6. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is ANSWER: Let the speed of the train be V Length of train = (V – 2)x 9/3600 km = (V – 4)x 10/3600 Solving, we get 9V – 18 = 10V – 40 Or, V = 22 Km/hr So, length of train = (22 – 2) x 9/ 3600 km = 50 m