Explanation

(a) Speed of wave on a string
$v = \sqrt{\frac{T}{m}}$
Or
$v \propto \sqrt{T}$
Or
$\frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}}$
Or
$T - \frac{2}{T_{1}} = \frac{v_{2}^{2}}{v_{1}^{2}}$
Or
$\frac{T_{2} - T_{1}}{T_{1}} = \frac{v_{2}^{2} - v_{1}^{2}}{v_{1}^{2}}$
Initially, $T_{1} = 120\ N,$
$v_{1} = 150ms^{- 1}$
$v_{2} = v_{1} + \frac{20}{100}v_{1}$
$= v_{1} + \frac{v_{1}}{5} = \frac{6v_{1}}{5}$
$= \frac{6}{5} \times 150 = 180ms^{- 1}$
So, from eq. (i), we get
$\frac{T_{2} - T_{1}}{T_{1}} = \frac{(180)^{2} - (150)^{2}}{(150)^{2}}$
$= \frac{30 \times 330}{150 \times 150} = 0.44$
Hence, % increases in tension
$= \left( \frac{T_{2} - T_{1}}{T_{1}} \right) \times 100 = 0.44 \times 100 = 44\%$