Explanation

(d) The apparent frequency heard by the stationary observer is
$v^{'} = v_{0}\left( \frac{v}{v - v_{s}} \right)$ …(i)
where,
$v_{0} =$ frequency of source
$v =$ velocity of sound
$v_{s} =$ velocity of source
According to problem
$v^{'} = v_{0} + \frac{50}{100}v_{0}$
$v^{'} = \frac{3}{2}v_{0}$
Substituting this value of $v'$ in (i), we get
$\frac{3}{2}v_{0} = \eta v_{0}\left( \frac{v}{v - v_{s}} \right)$
$3v - 3v_{s} = 2v \Rightarrow v = 3v_{s}$
$\Rightarrow v_{s} = \frac{v}{3} = \frac{330}{3}ms^{- 1} = 110ms^{- 1}$