If the simple interest on ₹ $x$ at a rate of $a \%$ for $m$ years is same as that on ₹ $y$ at a rate of $a^2 \%$ for $m^2$ years,then $x: y$ is equal to

At what rate per cent per annum will a sum of money double in $16$ years (in $.25$)?

The population of a city increases at the rate of $5 \%$ $p.a.$ If the present population of the city is $370440$,then what was its population (in $lakh$) $3$ years ago?

The annual payment of $Rs. 160$ in $5 \, \text{years}$ at $5 \%$ per annum simple interest will discharge a debt of (in $Rs.$):

Prabhat took a certain amount as a loan from a bank at the rate of $8 \%$ simple interest per annum and gave the same amount to Ashish as a loan at the rate of $12 \%$ per annum on simple interest. If at the end of $12$ years,he made a profit of $Rs. 320$ in the deal,what was the original amount (in $Rs.$)?

$A$ sum of $Rs. 1521$ is lent out in two parts in such a way that the simple interest on one part at $10 \%$ for $5 \,yr$ is equal to that of another part at $8 \%$ for $10 \,yr$. What will be the two parts of the sum?