When no current passes through the galvanometer, the bridge is balanced hence,
P
Q
=
R
S
⇒
24+X
10
=
84+Y
30
Also, applying Kirchhoffs law ΣiR=Σi′R′ (parallel) (X+24)+(84)+Y=3(10+30) ⇒X+Y=12 ...(i) and 3X−Y=12 ...(ii) From Eqs. (i) and (ii), we get X = 6, Y = 6 (neglecting negative value)