Ramesh and Upendra start walking towards each other from point A and

One big issue with this question is no mention of time, although we know the ratio of speeds, and thus the ratio of time used, we don't know if this is in minutes, hours, days, or years. Thus "x hours" does not have much meaning alone. However, we can still lay out an equation with an extra variable.

Start by setting the speeds of Ramesh and Upendra as 11 and 2, and the distance traveled would be 11 and 2. This is perfectly fine as everything is in ratios. Then with the new setup, Upendra's new speed would be 2x, so we have the ratio of times would be \(R:U = \frac{2}{11}:\frac{11}{2x}\).

Again we only have a ratio, we do not know exactly for how long each person traveled. Yet we can still use this ratio by multiplying another variable y, which would convert everything into hours. Then the times in hours would be \(\frac{2}{11}y\) hours and \(\frac{11y}{2x}\) hours, as the question mentioned the difference is x hours so we can finally setup the equation:

\(\frac{2}{11}y - x = \frac{11y}{2x}\).

Clean it up and put it in standard form: \(x^2 - \frac{2}{11}y*x + \frac{11}{2}y = 0\)

This equation has solutions only if the determinant is greater than 0: \(b^2 - 4ac \geq 0\)

\(\frac{4}{11^2}y^2 - 4*\frac{11}{2}y \geq 0\). Divide by y as y = 0 is not a meaningful value for this question.

\(y \geq \frac{11*11^2}{2} = \frac{11^3}{2}\)

Plug \(y = \frac{11^3}{2}\) back in, this is the scenario where we have only one solution for x. The constant term is \(\frac{11}{2}y = \frac{11^4}{4}\) which indicates one solution is \(11^2/2 = 60.5\). Looking at the answers we can only choose E.