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 $Rs.$):

The simple interest on a sum of money is $\frac{1}{9}$ of the principal and the number of years is equal to the rate per cent per annum. The rate per cent per annum is equal to

According to a census report,the population growth rate of Faridabad is going to be an increasing $A.P.$ with the first year's rate as $5 \%$ and common difference as $5 \%$,but simultaneously the migration rate is an increasing $G.P.$ with the first term as $1 \%$ and common ratio of $2$. If the population on $31 \, \text{December}, 2010$ is $1 \, \text{million}$,then find in which year will Faridabad witness its first fall in population?

$A$ person has left an amount of ₹ $1,20,000$ to be divided between his two sons aged $14$ years and $12$ years such that they get equal amounts when each attains $18$ years of age. If the amount gets a simple interest of $5 \%$ per annum,the younger son's share at present (in ₹) is

$A$ sum of money put at simple interest trebles itself in $15$ years. The rate per cent per annum is (in $\%$):

$A$ man invests a certain sum of money at $6 \%$ $p.a.$ simple interest and another sum at $7 \%$ $p.a.$ simple interest. His income from interest after $2$ $years$ was $Rs. 354$. One-fourth of the first sum is equal to one-fifth of the second sum. Find the total sum (in $Rs.$) he invested.