Question

A, B, and C enter into a partnership. A invests 3 times as much as B and B invests two-thirds of what C invests. At the end of the year, the profit earned is Rs. 6600. What is the share of B?

• A. 2400
• B. 6600
• C. 1200
• D. None of these
• E.

Hint:

To find the share in a partnership, calculate the ratio of each person's investment to the total investment, then multiply that ratio by the total profit.

Answer 1

The Correct Option is C

Step 1: Define the Investments

Let \( C \) represent C's investment.

B's investment is two-thirds of C's investment: \[ B = \frac{2}{3}C \]

A's investment is three times B's investment: \[ A = 3B = 3 \times \frac{2}{3}C = 2C \]

Step 2: Calculate the Total Investment \[ \text{Total Investment} = A + B + C = 2C + \frac{2}{3}C + C \] \[ = \frac{6C}{3} + \frac{2C}{3} + \frac{3C}{3} = \frac{11C}{3} \] Step 3: Determine the Ratio of Investments \[ A : B : C = 2C : \frac{2}{3}C : C \] Multiplying all terms by 3 to eliminate the fraction: \[ (2C \times 3) : \left(\frac{2}{3}C \times 3\right) : (C \times 3) = 6 : 2 : 3 \] Thus, the investment ratio is \( 6:2:3 \). Step 4: Calculate B's Share of the Profit

Total parts = \( 6 + 2 + 3 = 11 \)

B's share: \[ \left( \frac{2}{11} \right) \times 6600 = 1200 \]

Final Answer: \[ \boxed{1200} \]