Identify Ratio Parts

Let the shares of the three partners be $4x$, $12x$, and $5x$. The smallest share corresponds to $4x$ and the largest share corresponds to $12x$.

$\text{Ratio} = 4: 12: 5$

Set Up Equation for Difference

The difference between the largest share ($12x$) and the smallest share ($4x$) is given as ₹20208.

$12x - 4x = 8x = 20208$

Find the Value of One Unit ($x$)

Solve for $x$ by dividing ₹20208 by 8.

$x = \frac{20208}{8} = 2526$

Calculate Total Profit

The total profit is the sum of all three shares: $4x + 12x + 5x = 21x$. Substitute $x = 2526$.

$\text{Total Profit} = 21 \times 2526 = 53046$