A null point is found at 200cm in potentiometer when cell in...

Let potential gradient be $x$.

For the first case, we can write

$\dfrac{ε}{r + 5} \times 5 = 200x$ ......(1)

and after adding resistance, we can write

$\dfrac{ε}{r + 15} \times 15 = 300x$ .....(2)

From both equations, we get

$⇒ r = 5Ω$