At what rate per cent per annum will the simple interest on a sum of money be $\frac{2}{5}$ of the principal in $10$ $years$?

Nitin borrowed some money at the rate of $6 \% \text{ p.a.}$ for the first $3 \text{ years}$,$9 \% \text{ p.a.}$ for the next $5 \text{ years}$,and $13 \% \text{ p.a.}$ for the period beyond $8 \text{ years}$. If the total interest paid by him at the end of $11 \text{ years}$ is $₹ 8,160$,how much money (in $₹$) did he borrow?

Prabhat took a certain amount as a loan from a bank at the rate of $8 \%$ simple interest per annum and gave the same amount to Ashish as a loan at the rate of $12 \%$ per annum on simple interest. If at the end of $12$ years,he made a profit of $Rs. 320$ in the deal,what was the original amount (in $Rs.$)?

Manish borrowed a sum of $Rs. 1150$ from Anil at the simple rate of $6$ $p.c.p.a.$ for $3$ years. He then added some more money to the borrowed sum and lent it to Sunil for the same time at $9$ $p.c.p.a.$ at simple interest. If Manish gains $Rs. 274.95$ by way of interest on borrowed sum as well as his own amount from the whole transaction,then what is the sum (in $Rs.$) lent by him to Sunil?

Heena invests an amount of $10250$ at $4$ $p.c.p.a.$ to obtain a total amount of $Rs. 12710$ on simple interest after a certain period. For how many years did she invest the amount to obtain the total sum?

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