If the recurring decimal number $$3.7\overline{84}$$ is equal to the rational number $$\frac{p}{q}$$ and $$GCD(p, q) = 1$$,then $$p + q =$$

Let  x = $$3.7\overline{84}$$ 

We can write it as 

x = 3.7848484...

Multiply the equation with 10 on both the sides

10x = 37.8484... equation 1

Multiply equ 1 with 100 on both the sides

1000x = 3784.8484... equation 2

Subtract equation 1 from equation 2

1000x - 10x = 3784.8484... - 37.8484...

990x = 3747

x = $$\frac{3747}{990}$$

where $$\frac{3747}{990}$$ is in $$\frac{p}{q}$$ form

For $$GCD(p, q) = 1$$

$$\frac{3747}{990}$$ = $$\frac{1249}{330}$$

p + q = 1249 + 330

         = 1579

Hence, option B is correct answer.