**Explanation :**Speed of the train = (30 * 5/18) m / sec = (25/3) m/ sec.

Distance moved in passing the standing man = 100 m.

Required time taken = 100/(25/3) = (100 *(3/25)) sec = 12 sec

**Explanation :**Speed of train = 132 *(5/18) m/sec = 110/3 m/sec. Distance covered in passing the platform = (110 + 165) m = 275 m.

Time taken =275 *(3/110) sec =15/2 sec = 7 ½ sec

**Explanation :**Let the length of the train be x metres,

Then, the train covers x metres in 8 seconds and (x + 180) metres in 20 sec

\(\frac{x}{8}\) = \(\frac{(x+180)}{20}\)

20x = 8(x + 180) ---> x = 120.

Length of the train = 120 m. Speed of the train = (120/8) m / sec = m / sec = (15 *18/5) kmph = 54 km

**Explanation :**Speed of the train relative to man = (68 - 8) kmph

= (60* 5/18) m/sec = (50/3)m/sec

Time taken by the train to cross the man = Time taken by It to cover 150 m at 50/3 m / sec = 150 *3/ 50 sec = 9sec

**Explanation :**Speed of the train relative to man = (59 + 7) kmph

= 66 *5/18 m/sec = 55/3 m/sec.

Time taken by the train to cross the man = Time taken by it to cover 220 m

at (55/3) m / sec = (220 *3/55) sec = 12 sec

**Explanation :**Relative speed of the trains = (42 + 48) kmph = 90 kmph =(90*5/18) m / sec = 25 m /sec.

Time taken by the trains to'pass each other = Time taken to cover (137 + 163) m at 25 m /sec =(300/25) sec = 12 sec

**Explanation :**Relative speed of the trains = (72 - 54) km/hr = 18 km/hr = (18 * 5/18) m/sec = 5 m/sec.

Time taken by the trains to cross each other = Time taken to cover (100 + 120) m at 5 m /sec = (220/5) sec = 44 sec.

**Explanation :**Let the speed of the train be x kmph.

Speed of the train relative to man = (x + 5) kmph = (x + 5) * 5/18 m/sec.

Therefore 100/((x+5)*5/18)=6 <=> 30 (x + 5) = 1800 <=> x = 55

Speed of the train is 55 kmph.

**Explanation :**Let the length of train be x metres and length of platform be y metres.

Speed of the train relative to man = (54 - 6) kmph = 48 kmph = 48*(5/18) m/sec = 40/3 m/sec.

In passing a man, the train covers its own length with relative speed. Length of train = (Relative speed * Time) = ( 40/3)*12 m = 160 m.

Also, speed of the train = 54 *(5/18)m / sec = 15 m / sec.

(x+y)/15 = 20 <=> x + y = 300 <=> Y = (300 - 160) m = 140 m.

**Explanation :**Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph. Speed of goods train = (112 - 50) kmph = 62 kmph.