$A$ sum of ₹ $7700$ is to be divided among three brothers Vikas,Vijay,and Viraj in such a way that the simple interest on each part at $5 \%$ $p.a.$ after $1, 2,$ and $3$ years,respectively,remains equal. The share (in ₹) of Vikas is more than that of Viraj by:

Dalajit lent ₹ $10800$ to Jaabir for $3$ $years$ and ₹ $7500$ to Kabir for $2$ $years$ on simple interest and received ₹ $1422$ in all from both of them as interest. The rate of interest (in $\%$) per annum is

$A$ sum of ₹ $2800$ is divided into two parts in such a way that the interest on both the parts is equal. If the first part is lent at $9 \% \text{ p.a.}$ for $5 \text{ years}$ and the second part is for $6 \text{ years}$ at $10 \% \text{ p.a.}$,find the two sums.

Suhit borrowed a sum of $Rs. 6300$ from Vikas at the rate of $14 \%$ per annum for $3$ years. He then added some more money to the borrowed sum and lent it to Mohit at the rate of $16 \%$ simple interest for the same time. If Suhit gained $Rs. 618$ in the whole transaction,what sum did he lend (in $Rs.$) to Mohit?

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?

$A$ man invested $\frac{1}{3}$ of his capital at $7 \%$,$\frac{1}{4}$ at $8 \%$,and the remainder at $10 \%$. If the annual income is ₹ $561$,the capital (in ₹) is: