C and D invested ₹1,40,000 and ₹1,80,000, respectively. C remained for 9 months and D for 8 months. If C's share in the profit is ₹18,900, what is the total profit?

The correct option is ₹40,500.

Step-by-step Explanation:

Step 1: Understand the ratio of profit sharing
In a partnership business, the total profit is distributed among the partners in the ratio of the product of their investments and the time periods for which the amounts were invested.

Ratio of profit of C to D = (Investment of C × Time of C) : (Investment of D × Time of D)

Step 2: Calculate the ratio of investments multiplied by time
Investment of C = ₹1,40,000
Time period for C = 9 months
Investment of D = ₹1,80,000
Time period for D = 8 months

Equivalent investment of C = 1,40,000 × 9 = 12,60,000

Equivalent investment of D = 1,80,000 × 8 = 14,40,000

Ratio of Profit (C : D) = 12,60,000 : 14,40,000

Simplifying the ratio by dividing both sides by 1,80,000:

$\text{Ratio (C : D)}=\frac{1260000}{1440000}=\frac{7}{8}$

So, the profit sharing ratio between C and D is 7 : 8.

Step 3: Calculate the total profit
Let the total ratio parts be:

$\text{Total Parts}=7+8=15$

We are given that C's share in the profit is ₹18,900, which corresponds to 7 parts of the ratio.

$7\text{parts}=\text{₹18,900}$

Value of 1 part =

$\frac{18900}{7}=\text{₹2,700}$

Therefore, the total profit (15 parts) is:

$\text{Total Profit}=15\times 2700=\text{₹40,500}$

Thus, the total profit is ₹40,500.