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?

$A$ certain sum is invested for a certain time. It amounts to ₹ $450$ at $7 \%$ per annum. But when invested at $5 \%$ per annum,it amounts to ₹ $350$. Find the sum (in ₹).

$A$ person invested $\frac{2}{3}$ of his capital at $3 \%$,$\frac{1}{6}$ at $6 \%$,and the remainder at $12 \%$. If his annual income is $₹ 25$,then the total capital (in $₹$) is:

In simple interest rate per annum,a certain sum amounts to ₹ $5,182$ in $2$ $years$ and ₹ $5,832$ in $3$ $years$. The principal in rupees is:

The rate of interest on a sum is $4 \%$ per annum for the first $2$ years,$6 \%$ per annum for the next $4$ years,and $8 \%$ per annum for the period beyond $6$ years. If the simple interest accrued by the sum for a total period of $9$ years is ₹ $1120$,find the sum. (In ₹)

If the interest on ₹ $800$ is more than the interest on ₹ $400$ by ₹ $40$ in $2$ years,then the rate of interest (in $\%$) per annum is: