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.

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