As drummer does not hear any echo this means time between two successive wavefronts is equal to time in which a wavefront reaches back to drummer.

Distance covered by sound $=2 x$

If $v=$ speed of sound, then

$\frac{2 x}{v}=$ time interval between two successive wavefronts.

So, we have

In case I, $\frac{2 x}{v}=\frac{60}{40} \quad \dots(i)$

In case II, $\frac{2(x-90)}{v}=\frac{60}{60} \quad \dots(ii)$

Substituting for $x$ from Eq. $(i)$ in Eq. $(ii)$, we get

$2 x-180=v$

$\Rightarrow \frac{3}{2}-180=v$

$\Rightarrow v=360 \,ms ^{-1}$