**1. A train 100 m long is running at the speed of 30 km / hr. Find
the time ****taken by ****it to pass ****a man standing near the railway line.**

**Sol. **Speed of the train =
(30 x 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

** 2. A train is moving at a
speed of 132 km/hr. If the length of the train is ****110 ****metres, ****how long will it take to cross a railway platform 165 metres long?**

**Sol. **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

**3. A man is standing on a railway bridge which is 180 m long. He
finds ****that a train crosses the bridge in 20 seconds but himself in 8
seconds. Find ****the length of ****the train and its speed?**

**Sol. **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

*x/8=(x+180)/20 *ó 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

**4. A train 150 m long is running with a speed of 68 kmph. In ****what ****time will ****it pass a man who is running at 8 kmph in the same direction in
which ****the train ****is going?**

**Sol: **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 I =
Time taken by It to cover 150 m at 50/3 m */
*sec = 150 *3/ 50 sec = 9sec

**5. A train 220 m long is running with a speed of 59 kmph.. ****In what ****will ****it pass a man who is running at 7 kmph in the direction opposite to
that in ****which the train is going?**

**sol. **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

**6. Two trains 137 metres and 163 metres in length are running ****towards ****each ****other on
parallel lines, one at the rate of 42 kmph and another at 48 ****kmpb. In what time will they be clear of each other from the moment
they ****meet?**

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

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

**7. Two trains 100 metres and 120 metres long are running in the ****same ****direction ****with speeds
of 72 km/hr,In how much time will the first train cross the second?**

**Sol: **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.

**8. A train 100 metres long takes 6 seconds to cross a man walking
at 5 ****kmph in the direction opposite to that of the train. Find the speed
of the ****train.?**

**Sol**: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.

**9. A train running at 54 kmph takes 20 seconds to pass a platform.
Next it ****takes.12 sec to pass a man walking at 6 kmph in the same direction
in which the train is going . Find the length of the train and the length of
the platform.**

**Sol:**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.

**10. A man sitting in a train which is travelling at 50 kmph
observes that a ****goods ****train, ****travelling in opposite direction, takes 9 seconds to pass him. If
the goods train is 280 m long, find its speed.?**

**Sol**: Relative speed = 280/9 m / sec =
((280/9)*(18/5)) kmph = 112 kmph.

Speed of goods train = (112 - 50) kmph = 62 kmph.