An amount of Rs. 10 is lent to be returned in 11 monthly installments of Rs. 1…

Concept: Simple interest relates the final repayment Amount to the Principal by Amount = P + (P x R x T)/100, where R is the interest rate for whatever time unit T is measured in. When a loan is quoted as a single lump sum to be repaid (rather than as a reducing balance across several installments), the full repayment total is treated as the Amount in this equation, and T is taken in the same unit the rate is being asked for - here, months, since the question asks for a monthly rate.

Applying to this problem:

1. Principal P = Rs. 10 (the amount lent).

2. Total repayment (Amount) = 11 monthly installments of Rs. 1 each = Rs. 11.

3. Time T = 11 months - this already matches the monthly rate being asked for, so no unit conversion is needed.

4. Apply the amount formula: 11 = 10 + (10 x R x 11)/100.

5. Simplify the interest term: 11 - 10 = 1, so 1 = 110R/100, i.e. 1 = 1.1R.

6. Solve for R: R = 1/1.1 = 10/11.

Cross-check: Substituting back, 10 + (10 x 10/11 x 11)/100 = 10 + 100/100 = 10 + 1 = 11, which matches the total repayment of Rs. 11 - confirming the rate.

So the monthly rate of interest is 10/11%.