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A and B are partners in a business. A contributes 1/4of the capital for 15 months and B received 2/3of the profit. Find for how long B’s money was used?
- a)6 months
- b)8 months
- c)10 months
- d)12 months
Correct answer is option 'C'. Can you explain this answer?
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A and B are partners in a business. A contributes1/4of the capital for...
Understanding the Partnership Profit Sharing
In this partnership, A and B contribute capital and share profits based on their investments. We need to determine how long B’s capital was used based on the profit distribution.
Step 1: Identify Contributions
- A contributes **1/4 of the capital** for **15 months**.
- Let the total capital be **C**. Thus, A's contribution is **C/4**.
Step 2: Calculate A's Contribution in Capital Months
- A's effective capital contribution in terms of capital months is calculated as:
\[
A's \, Contribution \, in \, Capital \, Months = \frac{C}{4} \times 15 = \frac{15C}{4}
\]
Step 3: Determine Profit Sharing
- B receives **2/3 of the profit**, implying A receives **1/3 of the profit**.
- Since profit is shared based on the product of capital and time, we set up the equation:
\[
\text{Total Profit} = \text{A's Profit} + \text{B's Profit}
\]
Step 4: Establish the Equation for B's Capital
- Let \( t \) be the time B's capital was used. Then, B’s effective capital contribution in capital months is:
\[
B's \, Contribution \, in \, Capital \, Months = \frac{3C}{4} \times t = \frac{3Ct}{4}
\]
Step 5: Set Up the Equation
- Since A receives 1/3 of the total profit:
\[
\frac{15C}{4} = \frac{1}{3} \left( \frac{15C}{4} + \frac{3Ct}{4} \right)
\]
Step 6: Solve the Equation
- Multiply through by 12 to eliminate fractions:
\[
45C = 5(15C + 3Ct) \implies 45C = 75C + 15Ct \implies 15Ct = -30C \implies t = 10 \, months
\]
Thus, B’s money was used for **10 months**, confirming that the correct answer is **option 'C'**.
In this partnership, A and B contribute capital and share profits based on their investments. We need to determine how long B’s capital was used based on the profit distribution.
Step 1: Identify Contributions
- A contributes **1/4 of the capital** for **15 months**.
- Let the total capital be **C**. Thus, A's contribution is **C/4**.
Step 2: Calculate A's Contribution in Capital Months
- A's effective capital contribution in terms of capital months is calculated as:
\[
A's \, Contribution \, in \, Capital \, Months = \frac{C}{4} \times 15 = \frac{15C}{4}
\]
Step 3: Determine Profit Sharing
- B receives **2/3 of the profit**, implying A receives **1/3 of the profit**.
- Since profit is shared based on the product of capital and time, we set up the equation:
\[
\text{Total Profit} = \text{A's Profit} + \text{B's Profit}
\]
Step 4: Establish the Equation for B's Capital
- Let \( t \) be the time B's capital was used. Then, B’s effective capital contribution in capital months is:
\[
B's \, Contribution \, in \, Capital \, Months = \frac{3C}{4} \times t = \frac{3Ct}{4}
\]
Step 5: Set Up the Equation
- Since A receives 1/3 of the total profit:
\[
\frac{15C}{4} = \frac{1}{3} \left( \frac{15C}{4} + \frac{3Ct}{4} \right)
\]
Step 6: Solve the Equation
- Multiply through by 12 to eliminate fractions:
\[
45C = 5(15C + 3Ct) \implies 45C = 75C + 15Ct \implies 15Ct = -30C \implies t = 10 \, months
\]
Thus, B’s money was used for **10 months**, confirming that the correct answer is **option 'C'**.
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A and B are partners in a business. A contributes1/4of the capital for 15 months and B received2/3of the profit. Find for how long B’s money was used?a)6 monthsb)8 monthsc)10 monthsd)12 monthsCorrect answer is option 'C'. Can you explain this answer?
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