Two unknown resistances `X` and `Y` are placed on the left and right gaps of a meter bridge. The null point in the galvanometer is obtained at a distance of `80 cm` from left. A resistance of `100 Omega` is now connected in parallel across `X`. The null point is then found by shifting the sliding contact toward left by `20 cm`. Calculate `X` and `Y`.

Explanation

To solve the problem of finding the unknown resistances \(X\) and \(Y\) using a meter bridge, we can follow these steps:

### Step 1: Understand the initial conditions
In the first case, the null point is obtained at a distance of \(80 \, \text{cm}\) from the left. This means that the length of the wire on the left side (where resistance \(X\) is connected) is \(80 \, \text{cm}\) and the length on the right side (where resistance \(Y\) is connected) is \(20 \, \text{cm}\) (since the total length of the meter bridge is \(100 \, \text{cm}\)).

### Step 2: Apply the balance condition
According to the principle of the meter bridge (based on Wheatstone's bridge), the balance condition can be expressed as:
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