Question
      
        If a car covers $${\frac{2}{5}^{th}}$$ of the total distance with $${v_1}$$ speed and $${\frac{3}{5}^{th}}$$ distance with $${v_2}$$ then average speed is      
       A.
        $$\frac{1}{2}\sqrt {{v_1}{v_2}} $$              
       B.
        $$\frac{{{v_1} + {v_2}}}{2}$$              
       C.
        $$\frac{{2{v_1}{v_2}}}{{{v_1} + {v_2}}}$$              
       D.
        $$\frac{{5{v_1}{v_2}}}{{3{v_1} + 2{v_2}}}$$                 
              
            
                Answer :  
        $$\frac{{5{v_1}{v_2}}}{{3{v_1} + 2{v_2}}}$$      
             Solution :
        Average speed $$ = \frac{{{\text{Total distance travelled}}}}{{{\text{Total time taken}}}}$$
$$\eqalign{
  &  = \frac{x}{{\frac{{\frac{{2x}}{5}}}{{{v_1}}} + \frac{{\frac{{3x}}{5}}}{{{v_2}}}}}  \cr 
  &  = \frac{{5{v_1}{v_2}}}{{3{v_1} + 2{v_2}}} \cr} $$