Two unknown resistance are connected in the two gaps of a meter-bridge. The null point is obtained at $40 \mathrm{cm}$ from the left end. A $30 \mathrm{\Omega }$ resistance is connected in series with the smaller of the two resistances, the null point shifts by $20 \mathrm{cm}$ to the right end. What is the value of the smaller resistance (in $\mathrm{\Omega }$)?