Potentiometer problem

In the circuit of potentiometer, The length of the potentiometer wire $AB$ is $50cm$ .The emf of the battery $E_{1}$ is $4V$ , having negligible internal resistances.The values of resistances are $R_{1}$ and $R_{2}$ are $15\Omega$ and $5\Omega$ resp. When both the keys are open , the null point is obtained at a distance of $31.25cm$ from end A but when both the keys are $closed$ , the balance length reduces to $5cm$ only.Given $R_{AB}=10\Omega$ .The battery in secondary circuit has emf of $E_{2}V$ and internal resistance $r\Omega$ .

Find the balance length (in cm ) when key $K_{2}$ is open , and $K_{1}$ is closed .