Question

A is twice as fast as B and B is thrice as fast as C. The journey covered by C in 42 minutes will be covered by A in
A.7 minute
B.14 minutes
C.28 minutes
D.63 minutes

Answer 1

Hint: Here we may consider time taken by any one of A, B and C to be x and then we can express the time taken by the other two in the form of x and then calculate the value of this variable x using the conditions given in the question.

Complete step-by-step answer:
Let us consider the time taken by C to complete the journey be = x minutes.
Since, it is given that B is thrice as fast as C, it means that the time taken by B to complete this journey will be one-third of the time taken by the C.
So, time taken by B to complete the journey = $\dfrac{x}{3}$ minutes.
Also, it is given that A is twice as fast as B, it means that the time taken by A to complete this journey will be half of the time taken by the B.
So, time taken by A to complete the journey = $\dfrac{1}{2}\times \dfrac{x}{3}=\dfrac{x}{6}$ minutes. $\dfrac{1}{2}\times \dfrac{x}{3}=\dfrac{x}{6}$
Since, it is already given that the time taken by C to complete the journey is = 42 minutes.
So, we have the value of x = 42 minutes.
Therefore, the total time taken by A to complete the journey = $\dfrac{x}{6}=\dfrac{42}{6}=7$ minutes.
 Hence, option (a) is the correct answer.

Note: Students should note here that we could have put the value of x even in the first step that is while calculating the time taken by B to complete the journey and then divide the value obtained by 2 to get the value of time taken by A to complete the journey.