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Hi Vivek,
Let the total distance be D.
Let the point transversed half the distance by velocity V1.
Then the time required by it to do so = (D/2)/V1 = D/2V1
The remaining half was transversed by travelling at V2 for halftime and V3 velocity for another half time.
Let the time to cover the second half of the journey = t
Then V2t/2+V3t/2= D/2(Second Half of journey)
So t= D/(V2+V3)
The total time required for the journey is (D/2V1)+(D/(V2+V3))
The Average or mean Velocity = D/( (D/2V1) + (D/(V2+V3)) ) = 1/( (1/2V1) + (1/(V2+V3)) ) =2V1(V2+V3)/(2V1+V2+V3)----------(ans)
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