Let the total distance covered = L = Length of journey
According to the question,
(L/2 x 1/40) + (L/2 x 1/60) = 16

Correct Option: D

Let the total distance covered = L = Length of journey
According to the question,
(L/2 x 1/40) + (L/2 x 1/60) = 16
⇒ L/80 + L/120 = 16
⇒ (3L + 2L)/240 = 16
⇒ 5L = 16 x 240
∴ L = (16 x 240)/5 = 16 x 48 = 768 km

Time = Length of train / Relative speed

Correct Option: D

Relative speed = 20 + 1 = 21 km/h = 21 x 5/18 = 35/6 m/s
Time = Length of train / Relative speed = (350/35) x 6 = 60 s

Suppose length of the train = L m
Speed of the train = 60 km/h = 60 x 1000 = 60000 m/h
Length of tunnel = 1.5 km = 1500 m
Time taken by train = 2 min = 1/30 h

Correct Option: B

Suppose length of the train = L m
Speed of the train = 60 km/h = 60 x 1000 = 60000 m/h
Length of tunnel = 1.5 km = 1500 m
Time taken by train = 2 min = 1/30 h
Time = Distance/Speed
∴ 1/30 = L + 1500/60000
⇒ l = 500 m

Let the distance traveled on foot be x km
Then, distance converted by bicycle = (45 - x) km
∴ x/3 + (45 -x) /8 = 8³/₄ = 35/4

Correct Option: C

Let the distance traveled on foot be x km
Then, distance converted by bicycle = (45 - x) km
∴ x/3 + (45 -x) /8 = 8³/₄ = 35/4
⇒ (8x + 135 - 3x)/24 = 35/4
⇒ 5x + 135 = 210
⇒ 5x = 75
⇒ x = 15
∴ Distance converted by bicycle = (45 - 15) = 300 km

Let distance between Manipur and Dispur = D km
Average speed of train from Manipur = D/4 km/h
Average speed of train from Dispur = 2D/7 km/h
Let they meet T h after 6:00 am.
Then, according to the question,
(D/4 x T) + 2D/7 x (T - 2) = D

Correct Option: C

Let distance between Manipur and Dispur = D km
Average speed of train from Manipur = D/4 km/h
Average speed of train from Dispur = 2D/7 km/h
Let they meet T h after 6:00 am.
Then, according to the question,
(D/4 x T) + 2D/7 x (T - 2) = D
⇒ T/4 + 2(T - 2)/7 = 1
⇒ 7T + 8(T - 2) = 28
⇒ 15T = 44
∴ T = 44/15 h = 2h 56 min
Clearly, trains meet 2 h 56 min after 6:00 am.
It means the trains meet at 8:56 am.