correct answer is : b) 10 km

Explanation

Let, the distance between two place is ‘d’ km.
And the time taken by him is ‘t’ hour.
In 1^st case,
The man speed is 4 km/hr.
\therefore Time taken to covered distance = \frac{d}{4} hour \left[time\ =\ \frac{distance}{speed}\right]
In 2^nd case,
The man speed is 5 km/hr.
\therefore Time taken to covered distance = \frac{d}{5} hour \left[time\ =\ \frac{distance}{speed}\right]

According the qustions,
\frac{d}{4} - \frac{20}{60} = \frac{d}{5} + \frac{10}{60}
\rightarrow\ \frac{d}{4} - \frac{d}{5} = \frac{10}{60} + \frac{20}{60}
\rightarrow\ \frac{5d\ -\ 4d}{20} = \frac{10\ +\ 20}{60}
\rightarrow\ \frac{d}{20} = \frac{30}{60}
\rightarrow\ \frac{d}{20} = \frac{1}{2}
\rightarrow\ \ 2d = 20
\rightarrow\ \ d = \frac{20}{2}
\rightarrow\ \ d = 10 km
Ans: The distance between two place is 10 km.