If $$A = 0.142857142857$$ and $$B = 0.16666$$ ......, then what is the value of $$\frac{(A + B)}{AB}$$?

$$A=0.142857142857$$

or, $$1000000A=142857+0.142857$$

or, $$1000000A=142857+A$$

or, $$A=\frac{142857}{999999}$$

or, $$A=\frac{1}{7}.$$

Now, 

$$B=0.16666.........$$

or, $$100B=16+0.6666.........$$

or, $$100B=16+P\ \left(let\ say,\ P=0.6666....\right)$$

So, $$10P=6+0.66666.......$$

or, $$10P=6+P.$$

or, $$P=\frac{6}{9}=\frac{2}{3}.$$

So, $$100B=16+\frac{2}{3}=\frac{50}{3}.$$

or, $$B=\frac{1}{6}.$$

So, $$\frac{\left(A+B\right)}{AB}=\frac{\left(\frac{1}{6}+\frac{1}{7}\right)}{\frac{1}{6}.\frac{1}{7}}=\frac{\left(\frac{13}{6.7}\right)}{\left(\frac{1}{6.7}\right)}=13.$$

D is correct choice.