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

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.

$A$ sum of ₹ $1,550$ is lent out in two parts,one at $8 \%$ and another at $6 \%$. If the total annual income is ₹ $106$,find the money lent at each rate.

$A$ sum was doubled with $12 \frac{1}{2} \%$ rate of simple interest per annum. The time taken (in years) for that sum is:

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

Income of Hemant was Rs. $4000$. In the first $2$ years,his income decreased by $10\%$ and $5\%$ respectively,but in the third year,the income increased by $15\%$. What was his income (in Rs.) at the end of the third year?