Rajan invests an amount of INR 15,860 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
Step-by-step Solution:
Let the amounts invested for Rohan, Sohan, and Mohan be $P_1$, $P_2$, and $P_3$ respectively. The formula for Simple Interest is $I = \frac{P \times R \times T}{100}$. Since the interest amounts are equal: $$ \frac{P_1 \times 5 \times 2}{100} = \frac{P_2 \times 5 \times 3}{100} = \frac{P_3 \times 5 \times 4}{100} $$ Simplifying this, we get: $$ 10P_1 = 15P_2 = 20P_3 $$ Dividing by 5: $$ 2P_1 = 3P_2 = 4P_3 $$ To find the ratio $P_1 : P_2 : P_3$, we find the LCM of 2, 3, and 4, which is 12. $$ P_1 : P_2 : P_3 = \frac{12}{2} : \frac{12}{3} : \frac{12}{4} $$ $$ P_1 : P_2 : P_3 = 6 : 4 : 3 $$