$A$ 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 ₹).

$A$ sum of money invested at simple interest for two years at $5 \% \text{ p.a.}$ amounted to $Rs. 2750$. The rate at which the sum should have been invested to get $Rs. 300$ as interest after two years would be (in $\%$)?

$A$ sum of ₹ $1,550$ is lent out in two parts,one at $8 \%$ and another at $6 \%$. If the total annual income is ₹ $106$,find the money lent at each rate.

The rate of interest for the first $2$ years is $3 \%$ per annum,for the next $3$ years is $8 \%$ per annum,and for the period beyond $5$ years is $10 \%$ per annum. If a man gets $Rs. 1520$ as simple interest for $6$ years,how much money (in $Rs.$) did he deposit?

Sumit lends ₹ $10000$ for $2$ $years$ at $20 \%$ per annum simple interest. After $1$ $year,$ he receives ₹ $6000$. How much (in ₹) will he receive next year?

Arun invested a sum of money at a certain rate of simple interest for a period of $4$ years. Had he invested the same sum for a period of $6$ years,the total interest earned by him would have been $50$ percent more than the earlier interest amount. What was the rate of interest per cent per annum?