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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. What is the ratio of the speed of the train to that of the car?
  • a)
    3 : 4
  • b)
    2 : 3
  • c)
    1 : 2
  • d)
    1 : 3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
It takes eight hours for a 600 km journey, if 120 km is done by train ...
Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y=8      1/x + 4/y = 1/15 ...(i)
And, 200/x + 400/y = 25/3  1/x + 2/y = 1/24   ...(ii)
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.
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Most Upvoted Answer
It takes eight hours for a 600 km journey, if 120 km is done by train ...
Given data:
Distance = 600 km
Time taken for the journey = 8 hours
Let the speed of the train be ‘x’ km/hr and the speed of the car be ‘y’ km/hr.

Approach:
We have to solve the given problem using the following steps:
Step 1: Formulate the equations based on given data
Step 2: Solve the equations to find the values of x and y
Step 3: Calculate the ratio of the speed of the train to that of the car

Solution:
Step 1: Formulate the equations based on given data

According to the given data,
When 120 km is done by train and the rest by car:
Time taken = Distance/Speed
120/x + (600-120)/y = 8
Simplifying the above equation, we get:
120/x + 480/y = 8 …(1)

When 200 km is done by train and the rest by car:
Time taken = Distance/Speed
200/x + (600-200)/y = 8 1/3 = 25/3
Simplifying the above equation, we get:
200/x + 400/y = 25/3 …(2)

Step 2: Solve the equations to find the values of x and y

On solving equations (1) and (2), we get:
x = 60 km/hr
y = 80 km/hr

Step 3: Calculate the ratio of the speed of the train to that of the car

Ratio of the speed of the train to that of the car = x:y
= 60:80
= 3:4

Therefore, the correct answer is option A) 3:4.
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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. What is the ratio of the speed of the train to that of the car?a)3 : 4b)2 : 3c)1 : 2d)1 : 3Correct answer is option 'A'. Can you explain this answer?
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