The speeds of four cars are 2u, 3u, 4u and xu and the time taken by them to cover the same distance is xt, 4t, 3t and 2t respectively, where x, u, t are real numbers. What is the value of x?

Correct option is B

Given:

Speeds of four cars are 2u, 3u, 4u, and xu.

Time taken by them to cover the same distance is xt, 4t, 3t, and 2t respectively.

Where x, u, t are real numbers.

Concept Used:

Distance = Speed × Time

Solution:

Since the distance covered by all cars is the same:

Distance₁= Distance₂= Distance₃= Distance₄

Let d be the distance, then:

d = Speed₁× Time₁

=> d = 2u × xt

=> d = 2uxt

d = Speed₂× Time₂

=> d = 3u × 4t

=> d = 12ut

d = Speed₃× Time₃

=> d = 4u × 3t

=> d = 12ut

d = Speed₄× Time₄

=> d = xu × 2t

=> d = 2xut

Equating the distances:

2uxt = 12ut

=> 2ux = 12u

=> x = 12 / 2

=> x = 6

Hence, the correct answer is option b.