M and N contribute to a business investment in the ratio 2:7. They earn a profit of ₹81,000. M is a working partner and receives 15% of the profit extra. What is M's total share?

The correct option is ₹27,450.

Let's solve the problem step-by-step to find M's total share from the business profit.

Step 1: Calculate M's extra allowance for being a working partner.

The total profit earned by the business is ₹81,000.

As a working partner, M receives 15% of the total profit extra before the remaining profit is shared.

$\text{Extra amount for M}=15\%\text{of}\mathrm{81,000}$

$\text{Extra amount for M}=\frac{15}{100}\times \mathrm{81,000}=15\times 810=\text{₹}\mathrm{12,150}$

Step 2: Calculate the remaining profit to be distributed based on investment ratio.

$\text{Remaining Profit}=\text{Total Profit}-\text{Extra amount given to M}$

$\text{Remaining Profit}=\mathrm{81,000}-\mathrm{12,150}=\text{₹}\mathrm{68,850}$

Step 3: Calculate M's share from the remaining profit.

M and N contributed to the business in the ratio 2 : 7.

Total ratio parts = 2 + 7 = 9 parts.

M's share of the remaining profit is 2 parts out of 9:

$\text{M's profit share}=\frac{2}{9}\times \mathrm{68,850}$

$\text{M's profit share}=2\times \mathrm{7,650}=\text{₹}\mathrm{15,300}$

Step 4: Calculate M's total share.

M's total share consists of the extra allowance plus M's share from the remaining profit:

$\text{M's total share}=\text{Extra Allowance}+\text{M's profit share}$

$\text{M's total share}=\mathrm{12,150}+\mathrm{15,300}=\text{₹}\mathrm{27,450}$

Thus, M's total share is ₹27,450.