$A$ 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 ₹).

What annual payment (in $Rs.$) will discharge a debt of $Rs. 770$ due in $5$ years,the rate of interest being $5 \%$ per annum?

Arun lends ₹ $20,000$ to two of his friends. He gives ₹ $12,000$ to the first at $8 \%$ p.a. simple interest. Arun wants to make a profit of $10 \%$ on the whole. The simple interest rate $\%$ at which he should lend the remaining sum of money to the second friend is

$A$ 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 $Rs.$).

Peter invested an amount of ₹ $12,000$ at the rate of $10 \%$ $p.a.$ simple interest and another amount at the rate of $20 \%$ $p.a.$ simple interest. The total interest earned at the end of one year on the total amount invested became $14 \%$ $p.a.$ Find the total amount (in ₹) invested.

Dalajit lent ₹ $10800$ to Jaabir for $3$ $years$ and ₹ $7500$ to Kabir for $2$ $years$ on simple interest and received ₹ $1422$ in all from both of them as interest. The rate of interest (in $\%$) per annum is