Ram divided $2189$ into three parts such that the simple interest on them after $1, 2,$ and $3$ years respectively is equal. The rate of simple interest is $4\%$ per annum in all cases. The smallest part is (in $Rs.$):

$A$ 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?

The simple interest on a sum for $8$ years is ₹ $47500$. The rate of interest is $10 \%$ per annum for the first $5$ years and $15 \%$ per annum for the next $3$ years. What is the value (in ₹) of the sum?

What is the simple interest (in ₹) on ₹ $5400$ in $5$ years at the rate of $12 \%$ per annum?

The population of a particular area of a city is $5000$. It increases by $10 \%$ in $1^{st} \,yr$. It decreases by $20 \%$ in the $2^{nd} \,yr$ because of some reason. In the $3^{rd} \,yr$ the population increases by $30 \%$. What will be the population of the area at the end of $3$ $years$?

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 ₹)