Apart from Preposition and First order logic, there are Temporal logic, Second Order logic and Fuzzy logic, that are not in GATE syllabus. You will study these things in Masters.
If you want to go deeper, there is advance method named Resolution Refutation that works for such statements.
speed of slowest runner = x m/m
speed of fastest runner = 2x m/m
fastest runner will run with a relative speed of 2x - x = x with respect to slowest runner.
They meet after 6th minute. That means this is the 2nd round of fastest runner and it's the 1st round of slowest runner.
so the relative distance covered by fastest runner in 6 minutes will be 400m with respect to slowest runner.
we know, distance = speed * time
400 = x * 6
x = 400/6.
Hence speed of fastest runner = 2 x = 400 / 3.
Hence time taken to cover 1600 metres:
time = distance / speed
time = 1600/ (400/3)
time = 12 minutes.
There few grammars where you can not remove ambiguity by applying anything.
An example of an inherently ambiguous language is the union of with . This set is context-free, since the union of two context-free languages is always context-free. But it is proved that there is no way to unambiguously parse strings in the (non-context-free) common subset .