A sum of Rs. 10 is lent by a child to his friend to be returned in 11 monthly instalment a of Rs. 1 each, the interest being simple. The rate of interest is:

Answer: Option B

Let the rate of interest be R% per annum = Amount to be paid. If paid at the end of 11 months
$$\Rightarrow 10+\frac{10\times R\times \frac{11}{12}}{100}=10+\frac{11R}{120}$$
Total effective payments = (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 month) + Rs. 1
$$\begin{array}{rl}& =\left(1+\frac{1\times R\times \frac{10}{12}}{100}\right)+\left(1+\frac{1\times R\times \frac{9}{12}}{100}\right)+.....+\left(1+\frac{1\times R\times \frac{1}{12}}{100}\right)+1\\ & =\left(1+\frac{10R}{1200}\right)+\left(1+\frac{9R}{1200}\right)+.....+\left(1+\frac{R}{1200}\right)+1\\ & =11+\frac{R\left(\frac{10\times 11}{2}\right)}{1200}\\ & =11+\frac{11R}{240}\\ & \text{Now we have}\\ & 10+\frac{11R}{120}=11+\frac{11R}{240}\\ & \frac{11R}{240}=1\\ & R=\frac{240}{11}\\ & \boxed{R=21\frac{9}{11}\%}\end{array}$$