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:

$A$ sum of ₹ $25400$ was lent out in two parts,one at $12 \%$ and the other at $12 \frac{1}{2} \%$. If the total annual income is ₹ $3124.2$,the money lent at $12 \%$ is (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?

What annual payment (in $Rs.$) will discharge a debt of $Rs. 1092$ due in $2 \,yr$ at $12 \%$ simple interest?

In how many years will ₹ $150$ produce the same interest at $8 \%$ per annum as ₹ $800$ produces in $3$ years at $4 \frac{1}{2} \%$ per annum?

$A$ man buys a watch for ₹ $1950$ in cash and sells it for ₹ $2200$ at a credit of $1$ $year$. If the rate of interest is $10 \%$ $p.a.$,what is his profit or loss?