It takes eight hours for a 600 km journey, if 120 km is done by train and the…

2023

It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:

  1. A.

    2 : 3

  2. B.

    3 : 2

  3. C.

    3 : 4

  4. D.

    4 : 3

Attempted by 1 students.

Show answer & explanation

Correct answer: C

Step-by-Step Solution

Let the speed of the train be t km/hr and the speed of the car be c km/hr.

  1. Set up the first scenario:

    • Distance by train = 120 km, Distance by car = 600 - 120 = 480 km.

    • Total time = 8 hours.

    • Equation 1: (120 / t) + (480 / c) = 8

    • Simplify by dividing by 40: (3 / t) + (12 / c) = 1/5 --- (Eq 1)

  2. Set up the second scenario:

    • Distance by train = 200 km, Distance by car = 600 - 200 = 400 km.

    • Total time = 8 hours + 20 minutes = 8 + 1/3 = 25/3 hours.

    • Equation 2: (200 / t) + (400 / c) = 25/3

    • Simplify by dividing by 25: (8 / t) + (16 / c) = 1/3 --- (Eq 2)

  3. Solve the system of equations:

    • From Eq 1: (3 / t) + (12 / c) = 0.2 => multiply by 4: (12 / t) + (48 / c) = 0.8

    • From Eq 2: (8 / t) + (16 / c) = 1/3 => multiply by 3: (24 / t) + (48 / c) = 1

    • Subtract the modified Eq 1 from modified Eq 2: [(24 / t) - (12 / t)] = 1 - 0.8 12 / t = 0.2 t = 12 / 0.2 = 60 km/hr.

  4. Find speed of the car (c):

    • Substitute t = 60 into Eq 1: (3 / 60) + (12 / c) = 1/5 1/20 + 12 / c = 1/5 12 / c = 1/5 - 1/20 = 3/20 3c = 240 => c = 80 km/hr.

  5. Calculate the ratio:

    • Ratio of speed of train to car = t : c = 60 : 80 = 3:4.

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