Answer:

Let, the distance between the two places = ‘D’ km.
In the 1st case,
Go from one place to another at the speed of 4 km/hr,
The time taken is = KaTeX parse error: KaTeX doesn't work in quirks mode. [time= KaTeX parse error: KaTeX doesn't work in quirks mode. ]
In the 2nd case,
Return from one place to another at the speed of 5 km/hr,
The time taken is = KaTeX parse error: KaTeX doesn't work in quirks mode. [time= KaTeX parse error: KaTeX doesn't work in quirks mode. ]
And there is 1 hour for taken rest between the two journeys.
According to the questions:
The total time taken is 10 hours at together.
So,
KaTeX parse error: KaTeX doesn't work in quirks mode.
=> KaTeX parse error: KaTeX doesn't work in quirks mode. = 10 [L.C.M of 4 & 5]
=> KaTeX parse error: KaTeX doesn't work in quirks mode. = 10
=> KaTeX parse error: KaTeX doesn't work in quirks mode. = 200 [cross multiplication]
=> KaTeX parse error: KaTeX doesn't work in quirks mode. = 200 – 20
=> KaTeX parse error: KaTeX doesn't work in quirks mode. = 180
=> 9D = KaTeX parse error: KaTeX doesn't work in quirks mode.
=> D = 20

Ans: The distance between the two places = 20 km.