A started a business with a capital of $\text{Rs. }1,12,000$. After $2$ months, B joined the business with a capital of $\text{Rs. }80,000$, and after another $2$ months, C joined the business with a capital of $\text{Rs. }72,000$. After $10$ months from the start of the business, B withdraws $\text{Rs. }8,000$ and C also withdraws $\text{Rs. }8,000$. If B received $\text{Rs. }9,800$ as his share in the profit at the end of a year, then the total profit was:

To find the profit-sharing ratio, we calculate the equivalent capital invested by each partner for $1$ month over a total period of $12$ months.
* A's Investment:
Invested $\text{Rs. }1,12,000$ for all $12$ months.

$$\text{Equivalent Capital}=1,12,000\times 12=13,44,000$$

* B's Investment:
Joined after $2$ months, so remained for $10$ months in total.
For the first $8$ months (from month $2$ to month $10$), capital = $\text{Rs. }80,000$.
For the next $2$ months (from month $10$ to month $12$), capital = $80,000-8,000=\text{Rs. }72,000$.

$$\text{Equivalent Capital}=(80,000\times 8)+(72,000\times 2)=6,40,000+1,44,000=7,84,000$$

* C's Investment:
Joined after another $2$ months (i.e., $4$ months from start), so remained for $8$ months in total.
For the first $6$ months (from month $4$ to month $10$), capital = $\text{Rs. }72,000$.
For the next $2$ months (from month $10$ to month $12$), capital = $72,000-8,000=\text{Rs. }64,000$.

$$\text{Equivalent Capital}=(72,000\times 6)+(64,000\times 2)=4,32,000+1,28,000=5,60,000$$

Now, find the ratio of their investments:

$$\text{A}:\text{B}:\text{C}=13,44,000:7,84,000:5,60,000$$

Dividing by $1,000$:

$$\text{A}:\text{B}:\text{C}=1344:784:560$$

Dividing by $16$:

$$\text{A}:\text{B}:\text{C}=84:49:35$$

Dividing by $7$:

$$\text{A}:\text{B}:\text{C}=12:7:5$$

Given that B's share of profit is $\text{Rs. }9,800$:

$$7\text{ units}=9,800⟹1\text{ unit}=\frac{9,800}{7}=1,400$$

The total profit corresponds to $12+7+5=24\text{ units}$:

$$\text{Total Profit}=24\times 1,400=\text{Rs. }33,600$$