Two unknown resistances  X and Y are connected to left and right gaps of a meter bridge and the balancing point is obtained 80cm from left when circuit is switched on. Now 10 ohm resistance is connected in parallel to X, it is observed that the balancing point is 50 cm from left when circuit is switched on. The values of X and Y respectively are

The balancing length in first case is  80cmBalancing length for meter bridge is RS=l100−l  XY=8020⇒X=4YWhen 10 Ω resistance is connected in parallel to X . The resistance of the left gap is  10X10+Xaccording to balancing condition of meter bridge  RS=l100−l10X10+XY=5050 RS=l'100−l' ,l' is given 50 cmOn solving above two equations we get X=30 Ω and  Y=7.5 ΩTherefore, the correct answer is (C).