Model 5 Train Vs Both platform and a man/a pole Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Rule 10 and Rule 1,

Let the length of train be x metre,

then, Speed of train

= $x/7 = {x + 390}/28$

$x = {x + 390}/4$

4x - x = 390

$x = 390/3$ = 130 metres

Answer: (a)

Relative speed of train

= (60 + 6) kmph.

=$({66 × 5}/18)$ m/sec.

= $55/3$ m/sec.

Length of train = 110 metre

∴ Required time = $(110/{55/3})$ seconds

= $({110 × 3}/55)$ seconds = 6 seconds

Answer: (d)

Rule 10 and Rule 1,

Let the length of train be x metres.

When the train crosses the standing man, its speed = $x/9$

When the train crosses the platform of length 84 m, its speed = ${x + 84}/21$

Obviously, $x/9 = {x + 84}/21$

21x - 9x = 9 × 84

12x = 9 × 84

$x = {9 × 84}/12$ = 63 m

Required speed

= $63/9$ m/sec = $63/9 × 18/5$ kmph

= 25.2 kmph

Answer: (b)

Rule 10 and Rule 1,

Let the length of the train be x metre

Speed of train when it crosses man = $x/10$

Speed of train when it crosses platform = ${x + 300}/25$

According to the question,

Speed of train

= $x/10 = {x + 300}/25$

25x = 10x + 3000

15x = 3000

$x = 3000/15$ = 200 metres

Length of train = 200 metre

Speed of train = $x/10 = 200/10$

= 20 m/sec

Time taken in crossing a 200 m long platform

= ${200 + 200}/20$ = 20 seconds

Answer: (c)

Let the length of train be x metres

According to question

Speed of the train = $x/10$ m/ sec.

Also, the speed of the train

= $({x + 50}/14)$ m/sec.

[Since, It passes the platform in 14 seconds]

Both the speeds should be equal,

i.e., $x/10 = {x + 50}/14$ = or 14x = 10x + 500

or 14x - 10x = 500

or 4x = 500

x = 125 metres

Hence, Speed = $125/10 = 12.5$ m/sec.

= ${12.5 × 18}/5$ km/hr. = 45 km/hr.

Answer: (b)

Rule 10 and Rule 1,

Let the length of train be x metre.

$x/15 = {x + 100}/25$

$x/3 = {x + 100}/5$

5x = 3x + 300

2x = 300

$x = 300/2$ = 150 metres