Correct Answer - Option 3 :

\(21 \frac{9}{11} \%\)
**Given :**

A sum of Rs. 10 is lend to be returned in 11 monthly instalments of Rs . 1 each interest being simple

**Formula used :**

Simple interest = P × R× T /100

Principal(P), Rate(R) and Time(T)

**Calculation :**

Let the rate of interest be R% per annum

⇒ Amount to be paid (if paid at the end of 11 months)

⇒ 10 + [10 × R × (11/12) / 100] = 10 + (11R/120)

⇒ Total effective payment = (Rs. 1 + interest on Rs. 1 for 10 months) + (Rs. 1 + interest on Rs. 1 for 9 months) + .... +(Rs. 1 + interest on Rs. 1 for 1 months) + Rs. 1

⇒ (1 + 1 × R × (10/12) / 100) + (1 + 1 × R × (9/12) / 100) + .... + (1 + 1 × R × (1/12) / 100) + 1

⇒ (1 + 10R/1200) + (1 + 9R/1200) + .... + (1 + R/1200) + 1

⇒ 11 + R(1 + 2 + .... + 10)/1200

⇒ 11 + R(10 × 11 / 2)/1200

⇒ 11 + R(10 × 11 / 2)/1200

⇒ 11 + 11R/240

Now we have,

⇒ 10 + 11R/120 = 11 + 11R/240

⇒ 11R/240 = 1

⇒ R = 240/11 = 21× 9/11%

**∴ Rate of interest is 21(9/11)%**