Let the speeds of two trains be x and y, respectively .
∴ Length of 1st train = 54x
Length of the 2nd train = 34y
According to the question.
(54x + 34y) / (x + y) = 46

Correct Option: A

Let the speeds of two trains be x and y, respectively .
∴ Length of 1st train = 54x
Length of the 2nd train = 34y
According to the question.
(54x + 34y) / (x + y) = 46
⇒ 54x + 34y = 46x + 46y
⇒ 27x + 17y = 23x + 23y
⇒ 4x = 6y
⇒ x/y = 3/2
∴ x : y = 3 : 2

The length of the fast train = Relative speed x Time
= (40 - 20) x (5/18) x 5

Correct Option: C

The length of the fast train = Relative speed x Time
= (40 - 20) x (5/18) x 5 = 27⁷/₉ m

Given that, t₁ = 6 s and t₂ = 9 s
Then, time taken by the trains to cross each other = 2t₁ t₂ / (t₂ - t₁)

Correct Option: B

Given that, t₁ = 6 s and t₂ = 9 s
Then, time taken by the trains to cross each other = 2t₁ t₂ / (t₂ - t₁)
= (2 x 6 x 9)/(9 - 6) = 36 s

If the trains meet after t h.
Relative speed of train = (24 -18) = 6 km/h
⇒ Distance = 27
∴ t = 27/6 = 9/2 h

Correct Option: B

If the trains meet after t h.
Relative speed of train = (24 -18) = 6 km/h
⇒ Distance = 27
∴ t = 27/6 = 9/2 h
∴ QR distance travel by train which is travelling at a speed of 18 km/h = 18t = 18 x 9/2 = 81 km

Let the speed of both trains be V km/h and (V + 6) km/h, respectively
Then, according to the question.
160 = V x 4 + (V + 6) x 4

Correct Option: C

Let the speed of both trains be V km/h and (V + 6) km/h, respectively
Then, according to the question.
160 = V x 4 + (V + 6) x 4
⇒ 160 = 4V + 4V + 24
⇒ 40 = V + V + 6
⇒ 2V + 6 = 40
⇒ 2V = 34
∴ V = 17
Hence, speeds of both the trains are 17 km/h and (17 + 6 ) km/h i,e 17 km/h and 23 km/h .