$A$ sum of $Rs. 725$ is lent in the beginning of a year at a certain rate of interest. After $8$ months,a sum of $Rs. 362.50$ more is lent but at the rate twice the former. At the end of the year,$Rs. 33.50$ is earned as interest from both the loans. What was the original rate (in $\%$) of interest?

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 $Rs.$)?

Simple interest on a certain sum is $\frac{16}{25}$ of the sum. If the rate per cent and time (in years) are equal,then the rate per cent is:

$A$ sum of $Rs. 15000$ amounts to an interest of $Rs. 4500$ in $5$ years. What is the rate of interest (in percentage)?

During the first year,the population of a village is increased by $5 \%$ and in the second year it is diminished by $5 \%$. At the end of the second year,its population was $47880$. What was the population at the beginning of the first year?

Ram deposited a certain sum of money in a company at $12 \%$ per annum simple interest for $4$ years and deposited an equal amount in a fixed deposit in a bank for $5$ years at $15 \%$ per annum simple interest. If the difference in the interest from the two sources is $Rs. 1350$,then the sum (in $Rs.$) deposited in each case is: