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Two unknown resistances are connected in...

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

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The correct Answer is:
24
`l_(x)=40 cm,l_(R)=60 cm` `(x)/(R)=(l_(x))/(I_(R))=(40)/(60)=(2)/(3)...........(i) `
`therefore (x+30)/(R)=(60)/(40)=(3)/(2)` `therefore (x+30)/(x)=(9)/(4)`
`9x=4x+120`
`5x=120 implies x=24 Omega`
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