Question

The speeds of three cars are in the ratio 4 : 3: 2. What is the ratio between the times taken by the cars to cover the same distance?
(a) 2 : 3 : 4
(b) 3 : 4 : 6
(c) 1 : 2 : 3
(d) 4 : 3 : 2

Answer 1

Hint: We will be using the concept of time, distance, and speed to solve the problem. Also, some concepts of ratio and proportion will be used to further simplify the question.

Complete step-by-step solution
We have been given that the ratio of speeds of three cars are 4 : 3: 2
So, let the speed of three cars be $4x,3x,2x$ respectively.
Now, we have to find the ratio of the time taken by three cars to cover a particular distance.
So, let us take the distance to be covered by the three cars be “d”.
Now, we know that the distance formula is given by,
$S\text{peed=}\dfrac{\text{Distance}}{\text{Time}}........(i)$
So, using formula (i) we can find the time taken by each of the three cars to cover distance “d”.
Time taken by Car 1 = $\dfrac{d}{4x}...........(ii)$
Time taken by Car 2 = \[\dfrac{d}{3x}...........(iii)\]
Time taken by Car 3 = \[\dfrac{d}{2x}............(iv)\]
Now we will make the denominator of equations (i), (ii), and (iii) all the same by multiplying in both numerator and denominator. So we have the ratio of time of three cars as $\dfrac{3d}{12x}:\dfrac{4d}{12x}:\dfrac{6d}{12x}$
Now canceling $\dfrac{d}{12x}$ in all the three-term we have the ratio as 3: 4: 6
Therefore the ratio of time taken by the cars to cover the same distance is 3: 4: 6.
Hence the correct option is (b).

Note: To solve these types of questions it is important to have a basic understanding of ratio and proportion. Also the solution can be shorten as
\[\text{Speed=}\dfrac{\text{Distance}}{\text{Time}}\]
\[\Rightarrow \text{Time=}\dfrac{\text{Distance}}{\text{Speed}}\]
Since distance is constant
\[\text{Time }\;\alpha\;\text{ }\dfrac{\text{1}}{\text{Speed}}\]
So, ratio of time is $\dfrac{1}{4}:\dfrac{1}{3}:\dfrac{1}{2}$ (or) $\dfrac{3}{12}:\dfrac{4}{12}:\dfrac{6}{12}$ (or) 3 : 4 : 6