Let there be $100$ factories in total.
Since there are $60$ workers / factory, so total workers = $60*100 = 6000$
Out of which $64.6\%$ of workers work in “Wholly private” factories i.e. $6000*0.646 = 3876$ workers
Now “Wholly private” have 90.3 factories,
So $\#$workers/factory = $\frac{3876}{90.3} = 42.92 \approx 43$ workers.