Three partners A, B and C entered into a business. A invested one-third of the capital for one-third duration. B invested one-fourth of the capital for one-fourth duration. C invested the remaining capital for the whole duration. Out of a profit of ₹17,000, how much profit will C get?

EXPLANATION

The correct option is (a) - ₹12,000.

[as per provisional answerkey]

Solution

In a partnership, the profit is shared in the ratio of the product of (Capital × Time Duration). Let the total capital be 12 units and the total duration be 12 months (using the LCM of 3 and 4 to simplify calculations).

Step 1: Calculate the investment and time for each partner.
Partner A:
Capital = 1/3 of 12 = 4 units
Time = 1/3 of 12 = 4 months
Product (A) = $4 \times 4 = 16$

Partner B:
Capital = 1/4 of 12 = 3 units
Time = 1/4 of 12 = 3 months
Product (B) = $3 \times 3 = 9$

Partner C:
Remaining Capital = $12 - (4 + 3) = 5$ units
Time = Whole duration = 12 months
Product (C) = $5 \times 12 = 60$

Step 2: Determine the Profit Sharing Ratio.
Ratio A : B : C = $16 : 9 : 60$
Sum of the ratios = $16 + 9 + 60 = 85$ units

Step 3: Calculate C's share of the total profit.
Total Profit = ₹17,000
C's share = $(60 / 85) \times 17, 000$
C's share = $60 \times (17, 000 / 85)$
C's share = $60 \times 200$ = ₹12,000

Why the other options are incorrect

Option (b) - ₹10,000: This value would be correct if C's ratio was 50 out of 85, but C's weighted contribution (5 units for 12 months) is significantly higher.
Option (c) - ₹12,500: This is a calculation error likely arising from miscalculating the remaining capital or the total sum of ratios (e.g., using 80 instead of 85).
Option (d) - ₹10,750: This figure does not correspond to the proportional division of 17,000 based on the derived ratio of 16:9:60.

Key Concept

In partnership problems, profit distribution is directly proportional to the product of the capital invested and the time period for which it was invested (Profit ∝ Capital × Time).