"at a height half of its speed is 10 m/s"
this is a confusing portion
"A stone thrown vertically upwards when particle is at a half height of its speed is 10 m/s then max height attained by particle is ....... ( S = 10 m/s2 )"
that is the half and height are interchanged while typing by mistake
let us consider the suitiation from the half height.
Now let us find the max. height it will travel from the half height.
h= (u^2)/2g = (10^2)/2*10 = 5
This is half the height. Then the complete height will be 10 m.
That is B option.
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