A man gets a simple interest of $\text{Rs. }3500$ on a certain principal at the rate of $10\%$ per annum in $5$ years. What compound interest will the man get on twice the principal in two years at the same rate?

**Step 1: Find the original principal ($P$)**
The formula for simple interest ($\text{SI}$) is:

$$\text{SI}=\frac{P\times R\times T}{100}$$

Given: $\text{SI}=3500$, $R=10\%$, $T=5$ years.

$$3500=\frac{P\times 10\times 5}{100}$$

$$3500=\frac{50P}{100}$$

$$3500=\frac{P}{2}$$

$$P=7000$$

Step 2: Find the new principal and compound interest

* New Principal ($P^{\prime }$) = Twice the principal $=2\times 7000=\text{Rs. }14000$
* Time ($n$) = $2$ years
* Rate ($R$) = $10\%$ per annum

The formula for the total amount ($A$) under compound interest is:

$$A=P^{\prime }\times {\left(1+\frac{R}{100}\right)}^n$$

$$A=14000\times {\left(1+\frac{10}{100}\right)}^2$$

$$A=14000\times {\left(\frac{11}{10}\right)}^2$$

$$A=14000\times \frac{121}{100}$$

$$A=140\times 121=16940$$

Now, calculate the Compound Interest ($\text{CI}$):

$$\text{CI}=A-P^{\prime }$$

$$\text{CI}=16940-14000=\text{Rs. }2940$$

Thus, the compound interest is $\text{Rs. }2940$.