Rajan invests an amount of INR $15860$ in the names of his three sons Rohan, Sohan and Mohan in such a way that they get the same interest amount after two, three and four years respectively. If the rate of simple interest is $5%$, then the ratio of amounts invested among Rohan, Sohan and Mohan will be:

Simple interest is given by:

$SI=\frac{PRT}{100}$

Here, rate is same and interest is also same.

So, principal is inversely proportional to time.

Times are:

$2$ years, $3$ years and $4$ years.

Therefore, ratio of amounts invested is:

$\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$

LCM of $2,3,4$ is $12$.

Multiplying each term by $12$:

$6:4:3$