In a metre bridge [Fig], the gaps are closed by two resistances P and Q and the balance point is obtained at 40 cm. When Q is shunted by resistance of 10 Ω, the balance point shifts to 50 cm. The values of P and Q are

For the balance of metre bridgePQ=RS=4060=23or P=23Q……….(1)When Q is shunted by a resistance of 10 Ω then net resistance in this gap should be a parallel combination of Q and 10 Ω resistance i.e., 10Q /10 +Q).Now the balance shifts to 50 cm i.e., R = 50cm and S = 50 cm. In this caseP[10Q/(10+Q)]=5050=1……..(2)Substituting the value of  P from eq. (1) in eq. (2), we get(2/3)Q[10Q/(10+Q)]=1Solving we get Q=5ΩFrom eq. (1),  P=23×5=103Ω