Please follow attached fig.
Let length be LCM of 5,30 = 150
equal lengths are marked

Ans B

Since we are marking at the thirds and fifths, we take a stick length equal to the LCM of (3 and 5) i.e. 15 for ease of calculation/depiction.

So we will have 15 equal lengths of 1 unit each. I will represent each dash as 1 unit
_ _ _||_ _|_||_ _ _||_|_ _||_ _ _

I have marked the third positions by a single vertical line and the fifths by double vertical line. Let us list down the number of sticks of different lengths(count the number of dashes before a bar and in between bars to do so)

1 unit => 2
2 units => 2
3 units => 3

So maximum number of sticks of equal length = 3. Answer B

Since LCM of 3 and 5 is 15
So, let the length of stick be 15 units.
So, on division in thirds, stick will be broken at 5,10 units from left position
Again on division in fifths , stick will be broken at 3,6,9,12 units from left position.

So, lengths of parts will be 3-0, 5-3, 6-5, 9-6, 10-9, 12-10, 15-12 = 3,2,1,3,1,2,3

So the maximum number of equal parts are there each equal to 3 units.

Answer B