Explanation:

To determine how many years it will take for a sum of Rs. 9,500 to become Rs. 11,780 at an 8% simple interest rate, first compute the total interest needed and then use the simple interest formula.

- Calculate total interest:

- Final Amount = Principal + Interest

- Rs. 11,780 = Rs. 9,500 + Interest

- Interest = Rs. 11,780 - Rs. 9,500 = Rs. 2,280.

- Calculate the number of years (n) using the simple interest formula:

- Simple Interest (SI) = (Principal × Rate × Time) / 100

- 2,280 = (9,500 × 8 × n) / 100

- n = (2,280 × 100) / (9,500 × 8)

- n = 3.

- Hence, the correct option is Option:1 - 3.

- So, the time taken for Rs. 9,500 to amount to Rs. 11,780 at 8% per annum is 3 years.