One third of a certain journey is covered at the speed of 80 km/hr, one fourth of the journey at the speed of 50 km/hr And the rest at the speed of 100 km/hr, what will be the average speed (in km/hr) for the whole journey ?

Let the total distance = $$12x$$ km

Distance covered at 80 km/hr = $$\frac{12x}{3}=4x$$ km

=> Time taken = $$\frac{4x}{80}=\frac{x}{20}$$ hours

Distance covered at 50 km/hr = $$\frac{12x}{4}=3x$$ km

=> Time taken = $$\frac{3x}{50}$$ hours

Distance covered at 100 km/hr = $$12x-4x-3x=5x$$ km

=> Time taken = $$\frac{5x}{100}=\frac{x}{20}$$ hours

Thus, total time = $$\frac{x}{20}+\frac{3x}{50}+\frac{x}{20}$$

= $$\frac{x}{10}+\frac{3x}{50}=\frac{8x}{50}$$

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

= $$\frac{12x}{\frac{8x}{50}}$$

= $$12\times\frac{50}{8}=75$$ km/hr

=> Ans - (A)