A 15 Ω resistance is connected in the left gap and an unknown resistance less than 15 Ω is connected in the right gap of a metre bridge. When the resistances are interchanged, the balance point is found to shift by 20 cm. The unknown resistance is

It is clear from the figure given by you that, the balance point is at J1 initially . Now according to question, when the resistances are interchanged,the balance point will shift to J2 so that the length of the bridge wire between J1 and J2 is 20 cm. The balance points J1 and J2 must be equidistant from the mid point (50 cm mark) of the wire so that J1 is at 60 cm and J2 is at 40 cm
Thus,we have
            R/X =  60/40 = 6/4
Or, 15/X = 6/4
This gives X = 10 Ω
​Therefore the unknown resistance is 10 ohm.