In a partnership firm, A invests \(\frac{1}{6}\)th of the total investment for \(\frac{1}{6}\)th of the tenure. invests \(\frac{1}{3}\)rd of the total investment for \(\frac{1}{3}\)rd of the tenure while C invests the remaining part for the full duration. Out of total profit of Rs. 46,00,000, what shall be C's share?

The Correct answer is Option 4. 

Key Points

Partnership Profit Calculation

To determine C's share of the profit in the partnership firm, we need to calculate the effective capital contribution of each partner based on their investment and the duration for which they invested.

Let the total investment 

Investment by A:
⇒ A invests 1/6 of the total investment for 1/6 of the tenure.
⇒ Effective contribution of A: A's contribution = (1/6) × (1/6) = 1/36

Investment by B:
⇒ B invests 1/3 of the total investment for 1/3 of the tenure.
⇒ Effective contribution of B: B's contribution = (1/3) × (1/3) = 1/9

Investment by C:
⇒ C invests the remaining part of the total investment.
⇒ The remaining investment is: C's investment = I - (1/6)I - (1/3)I = I - (1/6)I - (2/6)I = I - (3/6)I = (3/6)I = (1/2)I

⇒ C invests for the full duration (1).
⇒ Effective contribution of C: C's contribution = (1/2) × 1 = 1/2

​Now, we can sum up the effective contributions:

⇒ A's contribution: 1/36
⇒ B's contribution: 1/9 = 4/36
⇒ C's contribution: 1/2 = 18/36
Total effective contributions:

⇒ Total = 1/36 + 4/36 + 18/36 = 23/36

C's share of the total profit can be calculated as follows:
⇒ C's share = (C's contribution / Total contributions) × Total profit

⇒ C's share = (18/36) / (23/36) × 46,00,000 = (18/23) × 46,00,000

Calculating C's share:
⇒ C's share = (18 × 46,00,000) / 23 = 82800000 / 23 ≈ 36,00,000

Thus, C's share of the profit is: 4) Rs. 36,00,000