$$\frac{1}{3}$$ part of a certain journey is covered with the speed of 25 km/hr, $$\frac{1}{2}$$ part of the journey is covered with the speed of 45 km/hr and the remaining part covered with the speed of 37.5 km/hr. What is the average speed (in km/hr) for the whole journey?

Let total distance covered in the journey be = $$6x$$ km

Distance covered with the speed of 25 km/hr = $$\frac{1}{3}\times6x=2x$$ km

Distance covered with the speed of 45 km/hr = $$\frac{1}{2}\times6x=3x$$ km

Thus, remaining distance covered with speed of 37.5 km/hr = $$6x-(2x+3x)=x$$ km

Now, total time taken throughout the journey = $$(\frac{2x}{25})+(\frac{3x}{45})+(\frac{x}{37.5})$$

= $$(\frac{6x}{75})+(\frac{5x}{75})+(\frac{2x}{75})=\frac{13x}{75}$$ hr

$$\therefore$$ Average speed = total distance / total time

= $$6x\div\frac{13x}{75}$$

= $$6x\times\frac{75}{13x}=34.61$$ km/hr

=> Ans - (B)