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 was put at simple interest at a certain rate for $4$ $years$. Had it been put at $2 \%$ higher rate,it would have fetched ₹ $56$ more. Find the sum (In ₹).

$A$ man invests ₹ $3965$ in the names of his three daughters,Neeta,Sita,and Gita,in such a way that they would receive the same amount after $2, 3,$ and $4$ years. If the rate of interest is $5 \%$ p.a.,then the amount (in ₹) invested for Neeta,Sita,and Gita is:

In what time (in $years$) will a sum of money double itself at the rate of $20 \%$ per annum 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?

An investor invested his savings in the stock market. The value of his investments increased by $12 \%$ and $9 \%$ in the first year and the second year respectively. If the value of his investments after two years became ₹ $97,664$,then how much had he invested (in ₹)?