This is a question based on relative speed concepts which in turn depends on the variation of distance with respect to speed, when time is kept constant.

When the time is constant, distance is directly proportional to speed. In other words, the ratio of distances travelled by two objects will be the same as the ratio of their speeds. In the question, it’s given that A travelled 20 miles before A and B met each other for the first time. Let us evaluate the statements now.

Using statement I alone, we know the ratio of the speeds. Because both A & B started together and also ended up at the same point (when they met), we can say that they both travelled for the same time.

Because time is constant, the distances travelled by them will be in the same ratio of the speeds. So,

\(D_a\) : \(D_b\) = 4:1.

But we know that \(D_a\) is 20. So, we will be able to find out \(D_b\). Hence, we will be able to find out one half of the length of the track – this is nothing but the sum of the distances travelled by A and B, right?

Therefore, we will be able to find out the length of the track uniquely (remember that, in DS, you don’t have to go for the exact answer all the time.). So, statement I alone is sufficient. Possible answer options are A or D. Options B, C and E can be eliminated.

Using statement II alone, we know that B has travelled a distance of 10 km by the time they meet for the second time. However, what will remain constant irrespective of the first or the second meeting is the ratio of their speeds.

Let the length of the track be 2πr. Then, distance travelled by A, between the first meeting and the second meeting = 2πr – 10. Now,

\(\frac{(2πr – 10)}{10}\) = \(\frac{20}{(πr – 20)}\).

Solving the above equation will definitely help us find a unique value of 2πr. Hence, statement II alone is also sufficient. Option A can be eliminated.

Correct answer option is D.

Although the second statement seems like it is not giving you much information, whatever information it is giving you is enough to solve the question, if you know the ratio concept highlighted throughout the solution.

Hope this helps!

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