A sound source is approaching the listener, the frequency of sound is 100 cps. While going away from the listener, it is 50 cps. The frequency when the observer moves with the source is 

From formula of Doppler's effect, 

$f\text{'}=f\left(\frac{v}{v-v_s}\right)\Rightarrow 100=\frac{fv}{v-v_s}$

$\Rightarrow v-v_s=\frac{fv}{100}$                             …(i)

In case of recession of source, $f\text{'}=f\left(\frac{v}{v+v_s}\right)\Rightarrow 50=\frac{fv}{v+v_s}$

$\Rightarrow v+v_s=\frac{fv}{50}$         …(ii)

From Eqs. (i) and (ii), we get 

$2v=\frac{3fv}{100}$

$\therefore f=\frac{200}{3}=66.67\mathrm{Hz}$