40 men can complete a work in 48 days. 64 men started and did the same work for x days. After x days, 32 men increased, so, the remaining work is completed in $$16\frac{2}{3}$$ days, then the value of x is

Let efficiency of work done by a man be 1 unit/day.

So, total units of work = $$40\times\ 48\times\ 1=1920$$ units

Now, if 64 men worked for x days, so amount of work done = $$64\left(x\right)\left(1\right)=64x$$ units

Now, after x days, total number of men = $$64+32=96$$

So, work done by these 96 men in $$16\ \dfrac{2}{3}$$ days = $$96\times\ 1\times\ 16\ \dfrac{2}{3}$$ units = $$96\times\ 1\times\ \dfrac{50}{3}=1600$$

So, we can say,

$$1920=64x+1600$$

or, $$1920-1600=64x$$

or, $$64x=320$$

or, $$x=\dfrac{320}{64}=5$$

So, value of $$x$$ is 5.