Assertion (A): If $\dfrac{a}{b} = \dfrac{c}{d}$, then $\dfrac{a+c}{b+d} = \dfrac{a}{b}$.

Reason (R): If two or more than two ratios are equal, then each ratio = $\dfrac{\text{sum of antecedents}}{\text{sum of consequents}}$.

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

We know that,

Each ratio = $\dfrac{\text{sum of antecedents}}{\text{sum of consequents}}$.

Let $\dfrac{a}{b} = \dfrac{c}{d}$ = k for some constant k.

a = kb, c = kd

Substituting value of a and c in $\dfrac{a+c}{b+d}$, we get :

$\Rightarrow \dfrac{kb + kd}{b + d} \\[1em] \Rightarrow \dfrac{k(b + d)}{(b + d)} \\[1em] \Rightarrow k \\[1em] \Rightarrow \dfrac{a}{b} \text{ or } \dfrac{c}{d}.$

∴ Both A and R are true, and R is the correct explanation of A.

Hence, option 1 is the correct option.