Three machines A, B and C working together can do a work in x hours. When working alone, A needs an additional 6 hours to do the work; B, one additional hour; and C, x additional hours. The value of x is

Time taken by the machines working together = $$x$$ hours

According to ques,

=> $$\frac{1}{x+6}+\frac{1}{x+1}+\frac{1}{x+x}=\frac{1}{x}$$

=> $$\frac{(x+6)+(x+1)}{(x+6)(x+1)}=\frac{1}{x}-\frac{1}{2x}$$

=> $$\frac{2x+7}{(x+6)(x+1)}=\frac{1}{2x}$$

=> $$4x^2+14x=x^2+7x+6$$

=> $$3x^2+7x-6=0$$

=> $$3x^2+9x-2x-6=0$$

=> $$(3x-2)(x+3)=0$$

=> $$x=\frac{2}{3},-3$$

$$\because$$ $$x$$ cannot be negative, hence $$x=\frac{2}{3}$$ hours

=> Ans - (A)