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 $12$:
$6:4:3$
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