Very hard question. Not for gmat I think.
In x minutes mini makes a questions.
i.e.Mini makes a question in x/a minutes.
In x minutes vinay makes a-y questions.
Vinay makes a question in x/(a-y) minutes
if mini makes a question in x/a-2 minutes (is equal to (x-2a)/a )and vinay makes a question in x/(a-y)-2 minutes is equal to ((x-2a+2y)/(a-y))than in x minutes mini makes 2y questions more.
That is to say problem wants a in this equation
solving for a for 2nd degree equations. (b^2-4ac formula)
Yes Sir, aftr lookin at the solution and the time constraint in the exam i too think it wont be asked in real exam..though it was put up in a mock test.