Profit Shares Calculation

First, determine the individual profit shares for M and N based on the total profit and the given difference.

• Let M's profit share be $P_M$ and N's profit share be $P_N$.
• Given the total profit is ₹1,494: $P_M + P_N = 1494$.
• Given M's share is ₹498 more than N's: $P_M = P_N + 498$.
• Substitute the second equation into the first: $(P_N + 498) + P_N = 1494$.
• Simplify the equation: $2P_N + 498 = 1494$.
• Solve for $P_N$: $2P_N = 1494 - 498 \implies 2P_N = 996 \implies P_N = \frac{996}{2} = 498$.
• Calculate $P_M$: $P_M = P_N + 498 = 498 + 498 = 996$.

Investment Ratio Determination

Establish the ratio between their profit shares and their capital contributions adjusted for the time period they invested.

• The ratio of profit shares is $P_M : P_N = 996 : 498$, which simplifies to $2 : 1$.
• Let M's capital contribution be $C_M$ and N's capital contribution be $C_N$.
• M invested for 3 months (Time$_M = 3$) and N invested for 4 months (Time$_N = 4$).
• Profit share is proportional to the product of capital and investment duration: $\frac{P_M}{P_N} = \frac{C_M \times \text{Time}_M}{C_N \times \text{Time}_N}$.
• Substitute the known profit ratio and time periods: $\frac{2}{1} = \frac{C_M \times 3}{C_N \times 4}$.
• This simplifies to the relationship: $8C_N = 3C_M$.

Capital Contribution Calculation

Use the information about the difference in capital invested and the derived ratio to find the specific capital contributed by M.

• We are given that M invested ₹48,000 more than N: $C_M = C_N + 48000$.
• Substitute this expression for $C_M$ into the ratio equation ($8C_N = 3C_M$): $8C_N = 3(C_N + 48000)$.
• Expand the equation: $8C_N = 3C_N + 144000$.
• Solve for $C_N$: $8C_N - 3C_N = 144000 \implies 5C_N = 144000$.
• Calculate N's capital contribution ($C_N$): $C_N = \frac{144000}{5} = 28800$.
• Finally, calculate M's capital contribution ($C_M$) using the given difference: $C_M = C_N + 48000 = 28800 + 48000 = 76800$.

Therefore, the capital contributed by M is ₹76,800.