Assertion (A) : The solution of : $\dfrac{x - 3}{x + 4} = \dfrac{x + 1}{x - 2}$ is 5.

Reason (R) : $\dfrac{ax + b}{cx + d} = \dfrac{p}{q}$.

⇒ q(ax + b) = p(cx + d)

This process is cross-multiplication.

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

2. Both A and R are correct, and R is not the correct explanation for A.

3. A is true, but R is false.

4. A is false, but R is true.

Given, $\dfrac{ax + b}{cx + d} = \dfrac{p}{q}$

On cross-multiplication,

⇒ q(ax + b) = p(cx + d)

So, reason (R) is true.

Given,

$\Rightarrow \dfrac{x - 3}{x + 4} = \dfrac{x + 1}{x - 2} \\[1em] \Rightarrow (x - 3) \times (x - 2) = (x + 4) \times (x + 1) \\[1em] \Rightarrow x(x - 2) - 3(x - 2) = x(x + 1) + 4(x + 1) \\[1em] \Rightarrow x^2 - 2x - 3x + 6 = x^2 + x + 4x + 4 \\[1em] \Rightarrow x^2 - 5x + 6 = x^2 + 5x + 4 \\[1em] \Rightarrow x^2 - 5x + 6 - x^2 - 5x - 4 = 0 \\[1em] \Rightarrow -10x + 2 = 0 \\[1em] \Rightarrow 10x = 2 \\[1em] \Rightarrow x = \dfrac{2}{10} = \dfrac{1}{5}.$

So, assertion (A) is false.

∴ A is false, but R is true.

Hence, option 4 is the correct option.