A sitar string gives a fundamental of 240 Hz when its tension is 50 N…

(a) $\dfrac{f'}{f} = \sqrt{\dfrac{T'}{T}}$. We want $T'$, so $T' = T\left(\dfrac{f'}{f}\right)^2 = 50\ \text{N} \times \left(\dfrac{300\ \text{Hz}}{240\ \text{Hz}}\right)^2 = 78.1\ \text{N}$.

(b) $\dfrac{L'}{L} = \dfrac{f}{f'} = \dfrac{240\ \text{Hz}}{300\ \text{Hz}} = 0.8$. The player presses the string so that four fifths of it vibrates.