NIMCET 2011 Question Paper with solutions

Let $\mathit{d}$ be the distance in first half and second half respectively of the journey. Time taken in first half and second half journey are $\frac{\mathit{d}}{{\mathit{v}}_1}$ and $\frac{\mathit{d}}{{\mathit{v}}_2}$ respectively.
$\therefore$ Average velocity
$=\frac{2\mathit{d}}{\frac{\mathit{d}}{{\mathit{v}}_1}+\frac{\mathit{d}}{{\mathit{v}}_2}}=\frac{2{\mathit{v}}_1{\mathit{v}}_2}{{\mathit{v}}_1+{\mathit{v}}_2}$