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:

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
$$\eqalign{ & = \left( {1 + \frac{{1 \times R \times \frac{{10}}{{12}}}}{{100}}} \right) + \left( {1 + \frac{{1 \times R \times \frac{9}{{12}}}}{{100}}} \right) + ..... + \left( {1 + \frac{{1 \times R \times \frac{1}{{12}}}}{{100}}} \right) + 1 \cr & = \left( {1 + \frac{{10R}}{{1200}}} \right) + \left( {1 + \frac{{9R}}{{1200}}} \right) + ..... + \left( {1 + \frac{R}{{1200}}} \right) + 1 \cr & = 11 + \frac{{R\left( {\frac{{10 \times 11}}{2}} \right)}}{{1200}} \cr & = 11 + \frac{{11R}}{{240}} \cr & {\text{Now we have}} \cr & 10 + \frac{{11R}}{{120}} = 11 + \frac{{11R}}{{240}} \cr & \frac{{11R}}{{240}} = 1 \cr & R = \frac{{240}}{{11}} \cr & \boxed{R = 21\frac{9}{{11}}\% } \cr} $$