The correct option is (B) [(50) / 3]Ω, [(50) / 2]Ω respectively.
Explanation:
Initially, jockey key at 40cm from P end i.e. (100 – 40) = 60cm from Q end
∴ (P/Q) = (40 / 60) = (2/3) (1)
Now Q is shunted with 50Ω.
∴ New resistance Q' = [(50Q) / (50 + Q)] and new balance point is moved by 10 cm.
Hence (P / Q') = (50 / 50) = 1
∴ P = Q' i.e. P = [(50Q) / (50 + Q)]
∴ (P/Q) = [(50) / (50 + Q)]
from (1),
(2/3) = [(50) / (50 + Q)]
∴ 100 + 2Q = 150
2Q = 50
Q = 25Ω
and P = (2/3)Q = (2/3) × 25 = (50 / 3)Ω