a, b, c and d are in proportion.

Assertion (A): a - c, c, b - d, d are in proportion.

Reason (R): a, c, b and d are in proportion.

1. Assertion (A) is true, but Reason (R) is false.

2. Assertion (A) is false, but Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Given,

a, b, c and d are in proportion.

$\therefore \dfrac{a}{b} = \dfrac{c}{d} \\[1em] \Rightarrow \dfrac{a}{c} = \dfrac{b}{d}.$

∴ a, c, b and d are in proportion.

So, reason (R) is true.

$\Rightarrow \dfrac{a}{c} = \dfrac{b}{d}\\[1em] \Rightarrow \dfrac{a}{c} - 1 = \dfrac{b}{d} - 1\\[1em] \Rightarrow \dfrac{a - c}{c} = \dfrac{b - d}{d}$

We can say that a - c, c, b - d, d are in proportion.

So, assertion (A) is true and reason (R) correctly explains assertion (A).

Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.