A man goes to Ahmedabad from Kolkata at a speed of 9km/hr and returns to Kolkata at a speed of 18km/hr, through same route. What is his average speed (in km/hr) of the entire journey?

Correct option is B

Given:

Speed from Kolkata to Ahmedabad(v$$_1$$) = 9 km/h,

Speed from Ahmedabad to Kolkata (v$$_2$$) = 18 km/h.

Formula Used: ​

Average speed =$$\frac{\text{Total distance}}{\text{Total time}}$$​

Solution:

The distance between Ahmedabad from Kolkata be (d) km.

Total distance = d + d = 2d

Time taken to go to the office:

t$$_1 = \frac{d}{v_1} = \frac{d}{9}$$​​

Time taken to return home:

t$$_2 = \frac{d}{v_2} = \frac{d}{18}$$​​

Total time =$$t_1 + t_2 = \frac{d}{9} + \frac{d}{18}$$​​

Total time =$$\frac{2d}{18} + \frac{d}{18} = \frac{3d}{18} = \frac{d}{6}$$​​​​

Average speed =$$\frac{2d}{\frac{d}{6}} = 2d \times \frac{6}{d} = 12 \text{ km/h}$$​   

Alternate Method: 

When distance is equal for speed a , and b then for 

Average speed = $$\frac{2ab}{a+b}$$​​

= $$\frac{2\times9\times18}{27} = 12 km/hr$$​​