CAT 2022 Slot 2 QA Question 3: Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative int

Question

Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative int

Accepted Answer

Let the total capital be $C$. The remaining part after investing one-fifth and one-third is:

$C(1 - \dfrac{1}{5} - \dfrac{1}{3}) = \dfrac{7C}{15}$

The annual simple interest from the three investments is:

$\dfrac{C}{5} 	imes \dfrac{6}{100} + \dfrac{C}{3} 	imes \dfrac{10}{100} + \dfrac{7C}{15} \

Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is