Explanation:

To find the total amount paid by Archana, we need to calculate the simple interest and add it to the principal loan amount.

- Loan amount: Rs 78,000

- Loan period: 24th January 2012 to 18th June 2012

- Time duration = 5 months (approximated to 5/12 years)

- Interest rate: Not given directly; needs calculation based on options

Formula for Simple Interest (SI):

$$\text{SI}=\frac{P\times R\times T}{100}$$

Where $P=78,000$, $T=\frac{5}{12}$

- Option 1: Total = 78,000 + SI = Rs 80,723

- Option 2: Total = 78,000 + SI = Rs 90,730

- Option 3: Total = 78,000 + SI = Rs 85,733

- Option 4: Total = 78,000 + SI = Rs 88,730

Upon calculating the simple interest using these options, the correct interest rate yields option 4.

- Correct Answer: Option 4 - Rs 88,730