M and N invest ₹80,000 and ₹1,20,000 respectively. After one year, profit including 8% simple interest on capital is ₹30,000. What is M's share?

Correct Answer: Option 2 (₹12,000)

Let's solve the problem step-by-step to calculate M's share of the profit.

Step 1: Understand the total investment and interest
Capital invested by M = ₹80,000
Capital invested by N = ₹1,20,000
Total Capital = ₹80,000 + ₹1,20,000 = ₹2,00,000

Simple interest is paid at 8% per annum on the capital invested by each partner before dividing the remaining profit according to their investment ratio.

Interest on M's capital = 8% of ₹80,000:

$\text{Interest for M}=\frac{8}{100}\times 80000=\text{₹}6400$

Interest on N's capital = 8% of ₹1,20,000:

$\text{Interest for N}=\frac{8}{100}\times 120000=\text{₹}9600$

Total interest given to M and N = ₹6,400 + ₹9,600 = ₹16,000

Step 2: Calculate the remaining profit to be shared
Total profit earned after one year = ₹30,000
Remaining profit after deducting interest on capital = ₹30,000 - ₹16,000 = ₹14,000

Step 3: Find the profit sharing ratio
The remaining profit is distributed in the ratio of their capital investments:

$\text{Ratio of M to N}=80000:120000=2:3$

Sum of ratio terms = 2 + 3 = 5

Step 4: Calculate M's share of the remaining profit

$\text{M's share of remaining profit}=\frac{2}{5}\times 14000=\text{₹}5600$

Step 5: Calculate M's total share
M's total share includes interest on capital plus M's share of the remaining profit:

$\text{M's total share}=\text{₹}6400+\text{₹}5600=\text{₹}12000$

Therefore, M's total share is ₹12,000.