Model 2 Train Vs Train in opposite direction Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Let the speed of second train be x m/s.

80 km/h = ${80 × 5}/18$ m/s

According to the question

$1000/{x + {80 × 5}/18}$ = 18

1000 = 18x + 400

x = $600/18$ m/s

= $600/18 × 18/5$ km/h = 120 km/h

Answer: (b)

Let train A start from station A and B from station B.

Let the trains A and B meet after t hours.

Distance covered by train A in t hours = 50t

Distance covered by train B in t hours = 60t km

According to the question,

60t - 50t = 120

t = $120/10$ = 12 hours.

Distance AB = 50 × 12 + 60 × 12

= 600 + 720 = 1320 km

Here, a = 60, b = 50, d = 120

Distance between A and B = $({a + b}/{a - b}) × d$

= $({60 + 50}/{60 - 50}) × 120$

= $110/10 × 120$ = 1320 km

Answer: (a)

If two trains be moving in opposite directions at rate u and v kmph respectively,

then their relative speed = (u + v) kmph.

Further, if their length be x and y km. then time taken to cross each other

= ${x + y}/{u + v}$ hours.

Here, Total length = 160 + 140 = 300m.

Relative speed = (77 + 67) kmph

= 144 kmph = 144 × $5/18$ m/s or 40 m/sec.

Time = $300/40 = 7{1}/2$ Seconds

Answer: (c)

Using Rule 3,

Relative speed = (50 + 58) kmph

= $(108 × 5/18)$ m/sec. = 30 m/sec

Required time

= $\text"Total length of trains"/ \text"Relative speed"$

= $({150 +180}/30)$ seconds

= $(330/30)$ seconds = 11 seconds

Answer: (d)

Let the trains meet each other after t hours.

Distance = Speed × Time

According to the question,

21t - 14t = 70

7t = 70 ⇒ t = $70/7$ = 10 hours

Required distance

= 21t + 14t = 35t = 35 × 10 = 350 km.

Using Rule 13,

Here, a = 21, b = 14, d = 70

Required distance

= $({a + b}/{a - b}) × d$

= $({21 + 14}/{21 - 14}) × 70$

= $35/7 × 70$ = 350 km.

Answer: (b)

Let P and Q meet after t hours.

Distance = speed × time

According to the question,

30t - 20t = 36

10t = 36 ⇒ t = $36/10$ = 3.6 hours

Distance between P and Q

= 30t + 20t

= 50t = (50 × 3.6) km. = 180 km.

Here, a = 30, b = 20, d = 36

Required distance

= $({a + b}/{a - b}) × d$

= $({30 + 20}/{30 - 20}) ×$ 36

= $50/10 × 36$ = 180 km