Question

A is twice as fast as B and B is twice as fast as C. The distance covered by C in $54\min $ will be covered by A in:
A. $216\min $
B. $27\min $
C. $108\min $
D. $13.5\min $

Answer 1

Hint: Here we can let the speed of C be $x{\text{ km}}/\min $ and then we can say that B and A will have the speed as $2x{\text{ and 4}}x$ because it is given in the question and therefore we can find their ratio of the time by using the formula ${\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}}$

Complete step by step answer:
Here we are given that A is twice as fast as B and B is twice as fast as C. The distance covered by C in $54\min $ is equal to the distance which A covers but we need to find the time in which A will cover the same distance.
So let us assume that the speed of C be $x{\text{ km}}/\min $
As we are given that B is twice as fast as C so we can say that:
Speed of B$ = 2x{\text{ km}}/\min $
Now A is twice as fast as B, so we can say that:
Speed of A$ = 2\left( {2x} \right) = 4x{\text{ km}}/\min $
Now we are given that time taken to cover the distance by C is $54\min $
We know that ${\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}}$
So for C ${\text{speed of C}} = \dfrac{{{\text{distance}}}}{{{\text{time of C}}}}$
$x = \dfrac{{{\text{distance}}}}{{54}}$
So we get the distance as $54x{\text{ km}}$
Now for A we can apply the formula as:
${\text{speed of A}} = \dfrac{{{\text{distance}}}}{{{\text{time of A}}}}$
As distance is same to be covered hence we can say that:
Speed of A$ = 4x$ and distance$ = 54x$
\[
  4x = \dfrac{{54x}}{{{\text{time of A}}}} \\
  {\text{time of A}} = \dfrac{{54x}}{{4x}} = 13.5\min \\
 \]

So, the correct answer is “Option D”.

Note: Here in the problems like this where we are given the relation between the parameters of the three persons or items, we just need to let any one of them as a variable and then convert the other two also in the form of that variable. So we can get the equation in the simple and a single variable.