A man goes to Jaipur from Surat at a speed of 3km/hr and returns to Surat at speed of 15km/hr, through same route. What is his average speed (in km/hr) of the entire journey?

Correct option is A

Given:

Speed from Surat to Jaipur (v$$_1$$) = 3 km/h,

Speed from Jaipur to Surat (v$$_2$$) = 15 km/h.

Formula Used: ​

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

Solution:

The distance between Surat and Jaipur  be (d) km.

Total distance = d + d = 2d

Time taken to go to the Jaipur:

t$$_1 = \frac{d}{v_1} = \frac{d}{3}$$​​

Time taken to return Surat

t$$_2 = \frac{d}{v_2} = \frac{d}{15}$$​​

Total time =$$t_1 + t_2 = \frac{d}{3} + \frac{d}{15}$$​​

Total time =$$\frac{5d}{15} + \frac{d}{15} = \frac{6d}{15} = \frac{2d}{5}$$​​​​

Average speed =$$\frac{2d}{\frac{2d}{5}} = 5 \text{ km/h}$$​   

Alternate Method: 

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

Average speed = $$\frac{2ab}{a+b}$$​​

= $$\frac{2\times3\times15}{3+15} = 5 km/hr$$