The sum of money that will produce ₹ $1770$ interest in $7 \frac{1}{2}$ years at $8 \%$ simple interest per annum is:

If the simple interest on ₹ $x$ at a rate of $a \%$ for $m$ years is same as that on ₹ $y$ at a rate of $a^2 \%$ for $m^2$ years,then $x: y$ is equal to

$A$ sum of money lent out at simple interest amounts to $Rs. 720$ after $2$ years and $Rs. 1020$ after a further period of $5$ years. Find the principal (in $Rs.$).

Sapna borrowed a certain sum of money from Kavita under the following repayment scheme based on simple interest: $8 \%$ $p.a.$ for the initial $2$ $years$,$9.5 \%$ $p.a.$ for the next $4$ $years$,$11 \%$ $p.a.$ for the next $2$ $years$,and $12 \%$ $p.a.$ after the first $8$ $years$. Find the total amount (in $Rs.$) which a sum of $Rs. 9000$ taken for $12$ $years$ becomes at the end of $12$ $years$.

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?

Shruti borrowed $Rs. 2500$ from her two friends. For one loan she paid $8 \%$ $p.a.$ and for the other $6 \%$ $p.a.$ simple interest. If she paid $Rs. 180$ as total interest for one year,how much did she borrow (in $Rs.$) at $8 \%$ $p.a.?$