Statement 1: In case of profit (i.e. if S.P. > C.P.), C.P. = S.P. x $\Big(\dfrac{100 \times \text{Profit}\%}{100}\Big)$.

Statement 2: In case of loss (i.e. if C.P. > S.P.), S.P. = $\Big(\dfrac{100 \times \text{C.P.}}{100 - \text{Loss}\%}\Big)$.

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

When S.P. > C.P., using formula

Profit = S.P. - C.P.

By formula,

$\Rightarrow \text{Profit}\% = \dfrac{\text{Profit}}{\text{C.P.}} \times 100\\[1em] \Rightarrow \text{Profit}\% = \dfrac{\text{S.P. - C.P.}}{\text{C.P.}} \times 100\\[1em] \Rightarrow \text{Profit}\% = \dfrac{\text{100 S.P. - 100 C.P.}}{\text{C.P.}}\\[1em] \Rightarrow \text{Profit}\% \times \text{C.P.} = \text{100 S.P. - 100 C.P.}\\[1em] \Rightarrow \text{Profit}\% \times \text{C.P.} + \text{100 C.P.} = \text{100 S.P.}\\[1em] \Rightarrow \text{C.P. (Profit\% + 100)} = \text{100S.P.}\\[1em] \Rightarrow \text{C.P.} = \dfrac{\text{100 S.P.}}{\text{(Profit\% + 100)}}\\[1em]$

So, statement 1 is false.

When C.P. > S.P.,

Loss = C.P. - S.P.

By formula,

$\Rightarrow \text{Loss}\% = \dfrac{\text{Loss}}{\text{C.P.}} \times 100\\[1em] \Rightarrow \text{Loss}\% = \dfrac{\text{C.P. - S.P.}}{\text{C.P.}} \times 100\\[1em] \Rightarrow \text{Loss}\% = \dfrac{\text{100 C.P. - 100 S.P.}}{\text{C.P.}}\\[1em] \Rightarrow \text{Loss}\% \times \text{C.P.} = \text{100 C.P. - 100 S.P.}\\[1em] \Rightarrow \text{100 S.P.} = \text{100 C.P.} - \text{Loss}\% \times \text{C.P.}\\[1em] \Rightarrow \text{100 S.P.} = \text{100 C.P.} - \text{Loss}\% \times \text{C.P.}\\[1em] \Rightarrow \text{100 S.P.} = \text{C.P. (100 - Loss\%)}\\[1em] \Rightarrow \text{S.P.} = \dfrac{\text{C.P. (100 - Loss\%)}}{100}\\[1em]$

So, statement 2 is false.

Hence, option 2 is the correct option.