Problem Analysis:

• The profit is distributed among three partners in the ratio 14 : 10 : 16.
• The difference between the smallest and largest shares is ₹29,547.
• We need to calculate the total profit.

Ratio Profit Distribution Calculation

Let the shares of the three partners be $14x$, $10x$, and $16x$, corresponding to the given ratio.

Identify Smallest and Largest Shares

• The smallest share corresponds to the smallest part of the ratio, which is 10. Share = $10x$.
• The largest share corresponds to the largest part of the ratio, which is 16. Share = $16x$.

Calculate Difference and Value of One Part

The difference between the largest and smallest shares is given as ₹29,547.

Mathematically, this is:

$16x - 10x = 29,547$

$6x = 29,547$

To find the value of one part ($x$), divide the difference by 6:

$x = \frac{29,547}{6}$

$x = 4924.5$

Calculate Total Profit

First, find the sum of the ratio parts:

Total ratio parts = $14 + 10 + 16 = 40$

The total profit is the sum of the ratio parts multiplied by the value of one part ($x$):

Total Profit = Total ratio parts $\times x$

Total Profit = $40 \times 4924.5$

Total Profit = $196,980$

Therefore, the total profit of the company is ₹196,980.