Four rational numbers p, q, r and s are such that q is the reciprocal of p and s is the reciprocal of r. The value of the expression $\Big([p + \dfrac{1}{q}] ÷ [r + \dfrac{1}{s}]\Big) ÷ \Big([s + \dfrac{1}{r}] ÷ [q + \dfrac{1}{p}]\Big)$ is equal to:

1. 1

2. 0

3. pr

4. $\dfrac{s}{q}$

Given,

$\Rightarrow q = \dfrac{1}{p} \\[1em] \Rightarrow \dfrac{1}{q} = p \\[1em] \Rightarrow s = \dfrac{1}{r} \\[1em] \Rightarrow \dfrac{1}{s} = r.$

Substituting value from above in given equation,

$\Rightarrow \Big([p + p] ÷ [r + r]\Big)÷ \Big([s + s] ÷ [q + q]\Big) \\[1em] \Rightarrow \Big(\dfrac{2p}{2r}\Big) ÷ \Big(\dfrac{2s}{2q}\Big) \\[1em] \Rightarrow \dfrac{p}{r} ÷ \dfrac{s}{q} \\[1em] \Rightarrow \Big(\dfrac{p}{r}\Big) \times \Big(\dfrac{q}{s}\Big) \\[1em] \Rightarrow \dfrac{p}{r} \times q \times \dfrac{1}{s} \\[1em] \Rightarrow \dfrac{p}{r} \times \dfrac{1}{p} \times r \\[1em] \Rightarrow 1.$

Hence, Option 1 is the correct option.