Work done by (x+4) men in (x+5) days is equal to the word done by (x-5) men is (x+20) days. Then the value of x is

Let Work done by $$(x+4)$$ men in $$(x+5)$$ days = 1 unit

$$=$$> Work done by 1 man in 1 day = $$\frac{\ 1}{\left(x+4\right)\left(x+5\right)}$$

Also Work done ny $$(x-5)$$ men in $$(x+20)$$ days = 1 unit

$$=$$> Work done by 1 man in 1 day = $$\frac{\ 1}{\left(x-5\right)\left(x+20\right)}$$

$$\therefore\ \frac{\ 1}{\left(x+4\right)\left(x+5\right)}=\frac{\ 1}{\left(x-5\right)\left(x+20\right)}$$

$$=$$>  $$\left(x+4\right)\left(x+5\right)=\left(x-5\right)\left(x+20\right)$$

$$=$$>  $$x^2+9x+20=x^2+15x-100$$

$$=$$>  $$6x=120$$

$$=$$>  $$x=20$$