Q. Ram and Shyam are running on different circular tracks. In the time that Ram completes 4 rounds of his track, Shyam completes 3 rounds of his track. If Ram and Shyam interchange their tracks, the time taken by both of them to complete 1 round is same. What is the ratio of speeds of Ram and Shyam?

A. \(\sqrt\)

B. \(\sqrt\)

C. \(\frac\)

D. \(\frac\)

E. Cannot be determined

C. \(\frac\)

On first reading, the way forward is not crystal clear but what makes it doable is that time being same, track length is proportional on speeds; and there is a second relation also … so two variables, two data seems doable.

Let the speeds of Ram and Shyam be x and y.

Using the first equation and equating the time,

\(\frac\) = \(\frac\)

\(\Rightarrow \frac=\frac\)

Next, the second data …

\(\frac\) = \(\frac\)

\(\Rightarrow \frac=\frac\)

From the two relations,

\(\frac\) = \(\frac\)

\(\frac\) = \(\frac\)