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**Hint:**Meter bridge: A meter bridge also called a slide wire bridge is an instrument that works on the principle of a Wheatstone bridge. A meter bridge is used in finding the unknown resistance of a conductor as that of in a Wheatstone bridge.

**Complete step-by-step solution:**

Given,

R=$10\Omega $

When a balance point is at 40cm, we have

$ \Rightarrow \dfrac{R}{S} = \dfrac{{40}}{{100 - 40}}$

Simplify,

$ \Rightarrow \dfrac{R}{S} = \dfrac{{40}}{{60}}$

$ \Rightarrow \dfrac{R}{S} = \dfrac{2}{3}$

$ \Rightarrow 3R = 2S$ …(1)

When a resistance of $10\Omega $is added in series with R, then equivalent resistance at R is${R^`} = R + 10$

Now, balance point is at 60 cm. So, we have

$ \Rightarrow \dfrac{{R + 10}}{S} = \dfrac{{60}}{{100 - 60}}$

$ \Rightarrow \dfrac{{R + 10}}{S} = \dfrac{{60}}{{40}}$

$ \Rightarrow \dfrac{{R + 10}}{S} = \dfrac{3}{2}$

$ \Rightarrow 2R + 20 = 3S$

$ \Rightarrow 2R - 3S = 20$ …(2)

Solving equation 1 and 2

S=$12\Omega $

R=$8\Omega $

**Note:**The device required in finding the unknown resistance of a conductor using the meter bridge are- meter bridge, resistance box, galvanometer, unknown resistance of length 1m, screw gauge, connecting wire, jockey, and one way key. A scale is attached to the block.

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