If Tanya walks at the speed of 6 km/h, she misses a train by 2 minutes. However, if she walks at the speed of 8 km/h, she reaches the station 3 minutes before the arrival of the train. The distance covered by Tanya to reach the station is:

Correct option is D

Given:
Speed of Tanya when she’s 2 min late = 6km/hr
Speed of Tanya when she’s 3 minutes early = 8km/hr
Formula Used:
Speed = $$\frac{Distance}{Time}$$​​
Solution:
Let the distance be x
Time taken by Tanya to reach = $$\frac{x}{6}$$​ hr
Then time taken by Train to leave = $$\frac{x}{6} - \frac{2}{60}$$​​
If Tanya walks at 8km/hr then time taken = $$\frac{x}{8}$$​ hr
Then time taken by Train to leave = $$\frac{x}{8} + \frac{3}{60}$$​​
But time  taken by train is equal in both cases, hence
​$$\frac{x}{8}+ \frac{3}{60} = \frac{x}{6} - \frac{2}{60} \\\ \\\frac{x}{6} - \frac{x}{8} = \frac{3}{60} + \frac{2}{60} \\\ \\\frac{(4x-3x)}{24} = \frac{(3+2)}{60} \\\ \\x= \frac{5}{60 }× 24= 2km$$​​