A started a business with a capital of ₹656,000. After 2 months, B joined him with a certain amount of capital. At the end of a year, the profit was shared in the ratio 6:5. How much (in ₹) did B invest?

1. A

   647200

2. B

   670900

3. C

   656000

4. D

   669500

Appeared in: DSSSB October 2024

Explanation

• In a compound partnership, profit is shared in proportion to the product of the capital invested and the duration of the investment.
• A's investment was for 12 months, while B joined after 2 months, so B's investment was for 10 months (12 - 2).
• The ratio of their effective investments is (A's Capital × A's Time) : (B's Capital × B's Time).
• Setting up the equation: (656,000 × 12) / (B's Capital × 10) = 6/5.
• Solving this equation for B's Capital gives ₹656,000.

Why Other Options Were Wrong

• Option A: This value is the result of an incorrect calculation. It does not follow the established formula for profit sharing in a compound partnership.
• Option B: This value is the result of an incorrect calculation. It may arise from misinterpreting the time periods or making an arithmetic error in the proportion.
• Option D: This value is the result of an incorrect calculation. It does not correctly apply the principle that profit is proportional to both capital and time.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Compound Partnership and Profit Sharing as background academic context rather than a clinical decision trigger.
• Understanding partnership profit sharing is crucial for anyone entering a business partnership to ensure fair distribution of earnings based on contribution.
• This concept is fundamental in business mathematics and finance, applicable to various investment scenarios beyond just business startups.
• The ability to calculate proportions and solve for unknown variables is a key skill in financial planning and analysis.

How to Approach the Question

• First, identify the type of partnership. Since the partners invested their capital for different durations, this is a compound partnership.
• Carefully list the capital and investment duration for each partner. Let the unknown capital be 'x'. A's time is 12 months; B's time is 10 months.
• Recall the formula for profit sharing in a compound partnership: Profit Ratio = (Capital1 × Time1) : (Capital2 × Time2).
• Set up the equation using the given profit ratio (6:5) and the values for capital and time.
• Solve the resulting algebraic equation for the unknown variable 'x' to find the amount B invested.

Concept Tested & Keywords

• Concept Tested: Compound Partnership and Profit Sharing
• Stem keywords: business, capital, profit, ratio, invest
• Lead-in keywords: How much
• Negative lead-in flag: false

Question ID

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