Prakash lends a part of ₹ $20,000$ at $8 \%$ simple interest and the remaining at $\frac{4}{3} \%$ simple interest. His total income after a year was ₹ $800$. Find the sum (in ₹) lent at $8 \%$ interest.

Income of Hemant was Rs. $4000$. In the first $2$ years,his income decreased by $10\%$ and $5\%$ respectively,but in the third year,the income increased by $15\%$. What was his income (in Rs.) at the end of the third year?

For what sum (in ₹) will the simple interest at $R \%$ per annum for $2$ years be $R$?

Dalajit lent ₹ $10800$ to Jaabir for $3$ $years$ and ₹ $7500$ to Kabir for $2$ $years$ on simple interest and received ₹ $1422$ in all from both of them as interest. The rate of interest (in $\%$) per annum is

Albert invested an amount of $x$ rupees in a fixed deposit scheme offering $10 \%$ per annum for the $1^{\text{st}}$ year and $15 \%$ per annum for the $2^{\text{nd}}$ year and received an amount of ₹ $20,240$ after two years. What is $x$ (in ₹)?

$A$ certain sum becomes $5$ times in $3$ years at simple interest. In how many years will it become $13$ times?