There is a theroem that "Mid point of hypotenous is equidistance from all vertices . "
So D is equidistance from A, B,C .
Given AB =100 KM , let BC =x km ; (where x < 100 [given] )
So using pythagorous theorem .
(2y)^2=(100)^2+(x)^2 ................................... (i)
As both B and C reach at the last point at the same time . so
(100+x)/ 61.875 = y/45 + y/55 ................................. (ii)
By solving equation (i) and (ii) . ...
x= 2.5 (y) -100
y = 169.99 and 52.31
so if y =169.99 then x =2.5(169.99)-100=324.975 (which is much larger than 100 . so this choice of y is out .)
y = 52.31 is satisfying all criteria .
as BD =y =52.31
So option (B) is correct .