# How to Solve Train Problems Easily in Competative Exams

Train problems are not difficult to solve in the examination. A student just have to understand the equation first to solve question because mostly speed related questions are asked mostly n this topic. So, here you can understand how to solve train problems easily with given solutions in these equations.

Nowadays, the question level has increased in competitive examinations. These questions have been asked in this blog that has come in the previous exam, where it has been told to solve these questions in a simple way. So practice these questions and bring good marks in the exam.

Click here to know some important **formulas of train problems** for instant solutions of problems on trains.

**Way to Solve Train Problems Easily**

Q.1. A train moves past a telegraph post and a bridge 264 m ling in 8 seconds and 20 seconds respectively. What is the speed of the train?

(A) 69.5 km/hr

(B) 70 km/hr

(C) 79 km/hr

(D) 79.2 km/hr

Ans . D

Let the length of the train be x metres and its speed by y m/sec.

They, $$ {x\over y}=8⇒x=8y $$

$$ Now, {x+264\over 20}= y⟺8y+264=20y⟺y=22. $$

$$∴ \ speed = 22 \ m/sec = \left( 22× {18\over 5} \right) km/hr=72.9 km/hr. $$

Q.2. A train takes 18 seconds to pass completely through a station 162m long and 15 second through another station 120 m long. The length of the train is :

(A) 70 m

(B) 80 m

(C) 90 m

(D) 100 m

Ans . C

Let the length of the train be x metres

$$∴ \ {x+162\over 18}= {x+120\over 15}⟺ 15(x+162)=18(x+120)⟺ x=90 \ m. $$

Q.3. How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

(A) 25

(B) 30

(C) 40

(D) 45

Ans . B

Speed of train relative to man = (63-3) km/hr = 60 km/hr

$$=\left( 60×{5\over 18} \right)m/sec= {50\over 3}m/sec $$

⸫ Time taken to pass the man $$=\left( 500×{3\over 50} \right)sec = 30\ sec $$

Q.4. A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger ?

(A) 3.6 sec

(B) 18 sec

(C) 36 sec

(D) 72 sec

Ans . C

Speed of train relative to jogger = (45-9) km/hr = 36 km/hr

$$=\left( 36×{5\over 18} \right)m/sec = 10\ sec $$

Distance to be covered = (240+120) m = 360 m.

⸫ Time taken $$\left( {36\over 10} \right)\sec = 36 \ sec$$

Q5. A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?

(A) 5 sec

(B) 6 sec

(C) 7 sec

(D) 10 sec

Ans . B

Speed of train relative to man = (60+6) km/hr = 66 km/hr

$$=\left( 66×{5\over 18} \right)m/sec = \left( {55\over 3} \right)\ m/sec $$

⸫ Time taken to pass the man $$=\left( 110 ×{3\over 55} \right)\sec = 6 \ sec$$

Q.6. Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively. In how much time will they cross each other, if they are running in the same direction ?

(A) 72 sec

(B) 132 sec

(C) 192 sec

(D) 252 sec

Ans . D

Relative speed = (45-40) kmph = 5 kmph = $$=\left( 5×{5\over 18} \right)m/sec = \left( {25\over 18} \right)\ m/sec $$

Total distance covered = Sum of lengths of trains = 350 m.

⸫ Time taken$$=\left( 350 ×{18\over 25} \right)\sec = 252 \ sec$$

Q.7. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite direction on parallel tracks. The time (in seconds) which they take to cross each other is :

(A) 9

(B) 9.6

(C) 10

(D) 10.8

Ans . D

Relative speed = (60+40) km/hr $$=\left( 100×{5\over 18} \right)m/sec = \left( {250\over 9} \right)\ m/sec $$

Distance covered in crossing each other = (140+160) m = 300 m

Required time $$=\left( 300×{9\over 250} \right)sec = \left( {54\over 5} \right)\ sec = 10.8 \ sec$$

Q.8. Two trains are moving in opposite directions@60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in second is :

(A) 36

(B) 45

(C) 48

(D) 49

Ans . C

Relative speed = (60+90) km/hr $$=\left( 150×{5\over 18} \right)m/sec = \left( {25\over 3} \right)\ m/sec $$

Distance covered = (1.10+0.9) km = 2 km = 2000.

Required time $$=\left( 2000 ×{3\over 125} \right)\sec = 48 \ sec$$

Q.9. A train 125m long passes a man, running at 5 kmph in the same direction in which the train is going, in 10 seconds. The speed of the train is :

(A) 45 km/hr

(B) 50 km/hr

(C) 54 km/hr

(D) 55 km/hr

Ans . B

Speed of the train relative to man $$ =\left({125\over 10} \right)m/sec=\left({25\over 2} \right)m/sec $$

$$ = \left( {25\over 2}×{18\over 5}\right) km/hr = 45 km/hr $$

Let the speed of the train be x kmph. Then, relative speed = (x-5) kmph.

⸫ x – 5 = 45 or x = 50 kmph.

Q.10. A train 110 m long passes a man, running at 6 kmph in the direction opposite to that of the train, in 6 second. The speed of the train is :

(A) 54 km/hr

(B) 60 km/hr

(C) 66 km/hr

(D) 72 km/hr

Ans . B

Speed of the train relative to man

$$ = \left( {110\over 6} \right)m/sec = \left( {110\over 6}×{18\over 5} \right) km/hr= 66 \ km/hr $$

Let the speed of the train be x kmph. Then, relative speed = (x+6) = kmph.

⸫ x+6 = 66 or x= 60 kmph.