A wheatstone bridge is used to determine the value of unknown resistance X by adjusting the variable resistance Y as shown in the figure. For the most precise measurement of X, the resistances P and Q:

Concept: 

The resistances in wheat stone bridge follows :

P/X = Q/Y     ----- (1) 

Explanation:

We know there is no current flows through galvanometer.

When current enters through the branch it is divided into two parts I1 and I2. the current flows through P  resistance is I1 and the current through the Q resistance is   I1. \(I_{1}P = I_{2}Q\)    ----- (2)

E = emf of battery and P,Q,X,Y are four resistances of circuit.

\(I_{1} = I_{3}, I_{2} = I_{4}\) so that we can calculate current,

\(I _{1} = \frac{E}{P+X}\) and \(I _{2} = \frac{E}{Q+Y}\)    ----- (3)

Then from equation (2) and (3) we get:  \(​​​​\frac{EQ}{Q+Y} = \frac{EP}{P+X}\)    ----- (4)

By solving equation 4 we get: 

P/X = Q/Y  so we can conclude that Resistance of P and Q should be roughly identical since it reduces experiment error.

Hence Option 3) is correct.