Question

A and B started a business in partnership by investing Rs 20,000 and Rs 15,000, respectively. After 6 months, C joined them with Rs 20,000. What is the share of B in the total profit of Rs 33,000 earned at the end of 2 years from the starting of the business?

• A. Rs 11,000
• B. Rs 9,600
• C. Rs 9,900
• D. Rs 10,000

Hint:

When calculating profit share in a partnership, use the effective capital invested by each partner, which is the product of their investment and time.

Answer 1

The Correct Option is C

Let the total profit be Rs 33,000, and the total time be 2 years.
The investments of A, B, and C are:
A's investment = Rs 20,000
B's investment = Rs 15,000
C's investment = Rs 20,000
Since C joined the business after 6 months, the time for each partner's investment is as follows:
A's time = 2 years = 24 months
B's time = 24 months
C's time = 18 months (as C joined after 6 months)
Now, we calculate the effective capital invested by each partner using the formula: \[ \text{Effective Capital} = \text{Investment} \times \text{Time} \] For A: \[ \text{Effective Capital of A} = 20,000 \times 24 = 480,000 \] For B: \[ \text{Effective Capital of B} = 15,000 \times 24 = 360,000 \] For C: \[ \text{Effective Capital of C} = 20,000 \times 18 = 360,000 \] The total effective capital is: \[ \text{Total Effective Capital} = 480,000 + 360,000 + 360,000 = 1,200,000 \] Now, the share of B in the profit is calculated by the ratio of B's effective capital to the total effective capital: \[ \text{Share of B} = \frac{\text{Effective Capital of B}}{\text{Total Effective Capital}} \times \text{Total Profit} \] \[ \text{Share of B} = \frac{360,000}{1,200,000} \times 33,000 = 9,900 \] Thus, the share of B in the profit is Rs 9,900.