Question

Three partners A, B, and C started a business. Twice A's investment is equal to thrice B's investment and B's investment is four times C's investment. Out of a total profit of ₹ 49500 at the end of the year, B's share in the profit is:

• A. ₹ 12,000
• B. ₹ 14,000
• C. ₹ 16,000
• D. ₹ 18,000

Hint:

For partnership problems, the share of profit is directly proportional to the investment ratio. Use the relationships given in the problem to express all investments in terms of one variable.

Answer 1

The Correct Option is D

Let the investments of A, B, and C be represented as \( a \), \( b \), and \( c \) respectively. The problem gives the following relationships: \[ 2a = 3b \quad \text{(Twice A's investment is equal to thrice B's investment)} \] \[ b = 4c \quad \text{(B's investment is four times C's investment)} \] Step 1: Express \( a \) and \( b \) in terms of \( c \): From \( b = 4c \), we substitute this into \( 2a = 3b \): \[ 2a = 3 \times 4c = 12c \quad \Rightarrow \quad a = 6c. \] Step 2: Now, the total investment is \( a + b + c \): \[ a + b + c = 6c + 4c + c = 11c. \] Step 3: The total profit is ₹ 49500, and the share of each partner is proportional to their investment. Thus, B's share in the profit is: \[ \frac{b}{a + b + c} \times 49500 = \frac{4c}{11c} \times 49500 = \frac{4}{11} \times 49500 = ₹ 18,000. \]