Question

A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined them after six months with an amount equal to that B. In what proportion should the profit at the end of one year be distributed among A, B and C?

• A. 3 : 5 : 2
• B. 3 : 5 : 5
• C. 6 : 10 : 5
• D. 3 : 7 : 8
• E. 6 : 10 : 3

Hint:

Always multiply the investment ratio by the time duration ratio to get the profit ratio. Be careful to calculate the time the money remained in the business, not the time passed before joining.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Three individuals invest money for different durations. We need to determine the ratio in which the total profit should be divided after one year.


Step 2: Key Formula or Approach:
In a partnership, the profit is distributed based on the "Effective Capital", which is the product of the invested amount and the time duration for which it was invested. \[ \text{Profit Ratio} = (I_A \times T_A) : (I_B \times T_B) : (I_C \times T_C) \]

Step 3: Detailed Explanation:
Let the initial investments of A and B be \(3x\) and \(5x\) respectively.
Since the profit is calculated at the end of one year (12 months): - A's investment duration (\(T_A\)) = 12 months. - B's investment duration (\(T_B\)) = 12 months.
C joins after 6 months with an amount equal to B's investment. - C's investment = \(5x\). - C's investment duration (\(T_C\)) = \(12 - 6 = 6\) months.
Now, calculate the effective capital for each partner: - A's effective capital = \(3x \times 12 = 36x\) - B's effective capital = \(5x \times 12 = 60x\) - C's effective capital = \(5x \times 6 = 30x\)
The profit-sharing ratio is the ratio of these effective capitals: \[ \text{A} : \text{B} : \text{C} = 36x : 60x : 30x \] Divide the ratio by their greatest common divisor, which is \(6x\): \[ \text{Ratio} = \frac{36x}{6x} : \frac{60x}{6x} : \frac{30x}{6x} \] \[ \text{Ratio} = 6 : 10 : 5 \]

Step 4: Final Answer:
The profit should be distributed in the proportion 6 : 10 : 5.