Initially, Aditya, Vishesh, and Nimesh shared profits equally, i.e., \(1:1:1\). Upon Aditya's death, Vishesh and Nimesh continue the business and share future profits in the ratio of \(4:3\).
The gaining ratio is calculated as the difference between the new ratio and the old ratio for each partner:
\[
\text{Gain of Vishesh: } 4 - 1 = 3.
\]
\[
\text{Gain of Nimesh: } 3 - 1 = 2.
\]
Thus, the gaining ratio of Vishesh and Nimesh = \(3:2\).
However, upon simplifying further, the ratio becomes:
\[
\text{Final Gaining Ratio} = \(5:2\).