Two cars are racing along two concentric circular paths. What is the r

Hi duahsolo,

The best approach to apply on DS word problems is to deconstruct the question before moving on to the statements.

Let the speed of the car on the outer circle be \(S_o\) and the speed of the car on the inner circle be \(S_i\). We need to ratio of the speed of the car on the outer circle to that on the inner circle, so we need \(S_o\)/\(S_i\). We have also been told that the times that both the cars take is a constant. Since Speed and Distance are directly proportional to each other and since the time is constant \(D_o\)/\(D_i\), where \(D_o\) is the distance traveled by the car on the outer circle and \(D_i\) is the distance traveled by the car on the inner circle.

The distance traveled by the car on the outer circle = Circumference of the outer circle = 2π * \(R_o\) ; \(R_o\) being the outer circle radius.
The distance traveled by the car on the inner circle = Circumference of the inner circle = 2π * \(R_i\) ; \(R_i\) being the inner circle radius.

\(D_o\)/\(D_i\)= (2π * \(R_o\)) / (2π * \(R_i\)) = \(R_o\)/\(R_i\).

So here if the statements give us the ratio of radii, we will be able to find the ratio of the distances and subsequently the ratio of speeds.

Statement 1 : The difference in the area between the outer circle and the inner circle is 192π

π(\(R_o\))^2 - π(\(R_i\))^2 = 192π.
Simplifying we get (R_o)^2 - (R_i)^2 = 192 -----> (\(R_o\) + \(R_i\))(\(R_o\) - \(R_i\)) = 192.
This does not give us enough information about the ratio of radii as there can be multiple values of \(R_o\) and \(R_i\). Insufficient.

Statement 2 : The difference in radius between the outer circle and the inner circle is 8

\(R_o\) - \(R_i\)= 8. This again does not give us enough information to determine the ratio. Insufficient.

Combining Statements 1 and 2

From Statement 1 we have (\(R_o\) + \(R_i\))(\(R_o\) - \(R_i\)) = 192 and from Statement 2 we have \(R_o\) - \(R_i\)= 8
Solving we get \(R_o\) + \(R_i\) = 24. Now since we have \(R_o\) - \(R_i\)= 8 and \(R_o\) + \(R_i\) = 24, we can solve to get definite values of radii which gives us a definite ratio. Sufficient.

OA : C

CrackVerbal Academics Team