Let frequency of tuning fork be \(f\).

From question we know the frequencies of sonometer wire \(\left(\frac{v}{21}\right)\) are \(\frac{v}{2 \times 0.2}\) and \(\frac{v}{2 \times 0.21}\)

\(\operatorname{Now} \frac{v}{0.4}-f=8\)

\(f-\frac{v}{0.42}=5 \quad \dots(ii)\)

Solving \((i)\) and \((ii)\), answer is \((c)\)