A boy goes three equal distance, each of length x km, with speed of y km/hr, $$\frac{3\text{y}}{5}$$ km/hr and $$\frac{2\text{y}}{5}$$ respectively. If the total time taken is 1 hour, then x : y is equal to :

Solution(By Examveda Team)

Total time taken :
$$\eqalign{ & = \left[ {\frac{x}{y} + \frac{x}{{\left( {\frac{{3y}}{5}} \right)}} + \frac{x}{{\left( {\frac{{2y}}{5}} \right)}}} \right]{\text{hours}} \cr & {\text{ = }}\left( {\frac{x}{y} + \frac{{5x}}{{3y}} + \frac{{5x}}{{2y}}} \right){\text{hours}} \cr & = \left( {\frac{{6x + 10x + 15x}}{{6y}}} \right){\text{hours}} \cr & = \left( {\frac{{31x}}{{6y}}} \right){\text{hours}} \cr & \therefore \frac{{31x}}{{6y}} = 1 \cr & \Leftrightarrow \frac{x}{y} = \frac{6}{{31}} \cr & \Leftrightarrow x:y = 6:31 \cr} $$