Total length of 5 pieces is 5 * 124 = 620.
To get maximum for shortest piece, we must max out all other pieces.

So let the longer three pieces be 140 each.
So the lengths are
a , b , 140, 140, 140.

Total length is 620
a + b + 140 + 140 + 140 = 620
a + b = 200.
Now to get the max length of the shortest piece we must max out these values and the way to do it is to make both lengths equal. that is a = b.
a + b = 200 -> a=100, b=100.

There are other combinations possible, but any other combination you take, one length will go down below 100 and that will become the shortest piece. So 100 is maximum possible length of the shortest piece.

mean = 124 and thus sum of 5 pieces = 124*5 = 620
let lengths in ascending order = a,b,c,d,e
given c=140, a+b+c+d+e = 620
to maximize a, minimize b,d,e. d and e should be at least equal to c and thus min possible value of d & e is 140
thus a+b+140*3=620
or a+b=200
now b>=a and to maximize a, let b=a and thus a=100
IMO B