Vikram covered 180 km distance in 10 hours. The first part of his journey he covered by Car, then he hired a Rickshaw. The speed of the car and rickshaw is 25 kmph and 15 kmph respectively. The ratio of the distances covered by the car and the rickshaw isa)7:9b)7:3c)7:5d)7:2e)7:4Correct answer is option 'C'. Can you explain this answer?

Question

Answer

let the time taken by car = x

then time taken by rickshaw would be = 10-x

Now,

distance = speed * time

180 = 25x + 15(10-x)

x=3 = time taken by the car.

7 = time taken by rickshaw.

Ratio of distance covered by Car/ rickshaw = (25*3)/(15*7) = 5/7 = 5:7

But there is no such option.

Answer

Given:
- Total distance covered by Vikram = 180 km
- Total time taken by Vikram = 10 hours
- Speed of car = 25 kmph
- Speed of rickshaw = 15 kmph

To Find: Ratio of distances covered by car and rickshaw

Solution:

Let's assume that Vikram covered 'x' km distance by car and 'y' km distance by rickshaw.

- As per the given condition, the total distance covered by Vikram is 180 km.

So, x + y = 180

- Also, we know that time = distance/speed.

The time taken by Vikram to cover the distance 'x' by car can be calculated as:

Time taken by car = distance/speed = x/25

Similarly, the time taken by Vikram to cover the distance 'y' by rickshaw can be calculated as:

Time taken by rickshaw = distance/speed = y/15

- As per the given condition, the total time taken by Vikram is 10 hours.

So, x/25 + y/15 = 10

Multiplying both sides by 75, we get:

3x + 5y = 750

- We can solve the above two equations to find the values of 'x' and 'y'.

Multiplying the first equation by 3, we get:

3x + 3y = 540

Subtracting this equation from the second equation, we get:

2y = 210

y = 105

Substituting the value of 'y' in the first equation, we get:

x + 105 = 180

x = 75

So, Vikram covered 75 km by car and 105 km by rickshaw.

- The ratio of distances covered by car and rickshaw can be calculated as:

Ratio = Distance covered by car : Distance covered by rickshaw = 75 : 105

Simplifying the ratio by dividing both sides by 15, we get:

Ratio = 5 : 7

Therefore, the correct option is (c) 7:5.

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