Explanation:

To find the sum invested, let's analyze the problem with simple interest formula:

- Simple Interest Formula: \( A = P + Prt \)

- \( A \) is the amount, \( P \) is the principal, \( r \) is the rate per annum, and \( t \) is time in years.

First Situation:

- Amount in 7 years: Rs.14,522

Second Situation:

- Amount in 11 years: Rs.18,906

Calculate Interest:

- Interest for 4 years (11 - 7 years) = Rs.18,906 - Rs.14,522 = Rs.4,384

- Annual Interest = Rs.4,384 / 4 = Rs.1,096 per year

Find Principal:

- Interest for 7 years = 7 * Rs.1,096 = Rs.7,672

- Principal (P) = Rs.14,522 - Rs.7,672 = Rs.6,850

Here’s the breakdown of options:

- Option 1: 6850 - Correct

- Option 2: 6900

- Option 3: 6800

- Option 4: 6750