Assertion (A) : 12 articles are bought for one rupee and 8 of them are sold for one rupee. Then gain% = 50%.

Reason (R) : Profit % = $\Big(\dfrac{\text{Profit}}{\text{C.P.}} \times 100\Big)\% \text{ and Loss}\% = \Big(\dfrac{\text{Loss}}{\text{C.P.}} \times 100\Big)\%$.

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.

If 12 articles are bought for ₹1, then:

C.P. per article = $\dfrac{1}{12}$ rupees

If 8 articles are sold for ₹ 1, then:

S.P. per article = $\dfrac{1}{8}$ rupees

Profit = S.P. - C.P.

$\text{Profit }= \dfrac{1}{8} - \dfrac{1}{12}\\[1em] = \dfrac{3 - 2}{24}\\[1em] = \dfrac{1}{24}$

Profit% = $\dfrac{\text{Profit}}{\text{C.P.}} \times 100$

$\text{Profit\% }= \dfrac{\dfrac{1}{24}}{\dfrac{1}{12}} \times 100\%\\[1em] = \dfrac{1 \times 12}{24 \times 1} \times 100\%\\[1em] = \dfrac{12}{24} \times 100\%\\[1em] = \dfrac{1}{2} \times 100\%\\[1em] = 50 \%$

So, assertion (A) is true.

Profit % = $\Big(\dfrac{\text{Profit}}{\text{C.P.}} \times 100\Big)\% \text{ and Loss}\% = \Big(\dfrac{\text{Loss}}{\text{C.P.}} \times 100\Big)\%$

These are the standard formula for finding profit% and loss%.

So, reason (R) is true but reason (R) does not clearly explains assertion (A) as there is no case of loss.

Hence, option 2 is the correct option.