Two moving coil galvanometer, \(X\) and \(Y\) have coils with resistance \(10 \Omega\) and \(14 \Omega\) cross-sectional areas \(4.8 \times 10^{-3} \mathrm{~m}^2\) and \(2.4 \times 10^{-3} \mathrm{~m}^2\), number of turns 30 and 45 respectively. They are placed in magnetic field of \(0.25 \mathrm{~T}\) and \(0.50 \mathrm{~T}\) respectively. Then, the ratio of their current sensitivities and the ratio of their voltage sensitivities are respectively

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.