A started a business with a capital of ₹520000. After 8 months, B joined him with a certain amount of capital. At the end of a year of A's starting the business, the profit was shared in the ratio 8:2. How much (in ₹) did B invest?

1. A

   373300

2. B

   397700

3. C

   386900

4. D

   390000

Appeared in: DSSSB 13 August 2024

Explanation

• The core principle is that profit sharing is proportional to the product of the capital invested and the duration of the investment.
• Partner A's investment was ₹520,000 for a full 12 months.
• Partner B joined after 8 months, so their investment was for a duration of 12 - 8 = 4 months.
• The profit ratio is given as 8:2, which simplifies to 4:1.
• The equation is set up as (520,000 × 12) / (B's Capital × 4) = 4/1.
• Solving this equation for B's Capital yields ₹390,000.

Why Other Options Were Wrong

• Option A: This value does not satisfy the profit-sharing equation. It is a result of a calculation error.
• Option B: This is an incorrect value that arises from miscalculation when solving the proportion.
• Option C: This incorrect value might be obtained if the time period for B's investment was miscalculated, for instance, using 8 months instead of 4 months.

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Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Partnership and Profit Sharing as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude, a non-nursing subject that frequently appears in nursing recruitment exams to assess analytical and problem-solving skills.
• Mastery of concepts like ratios and proportions is essential for tasks such as medication dosage calculation, where precision is critical for patient safety.
• What if B had joined after 4 months instead of 8? B's investment period would be 12 - 4 = 8 months. The equation would become (520,000 × 12) / (B's Capital × 8) = 4/1, which would result in B's capital being ₹195,000.

How to Approach the Question

• First, identify the capital invested and the duration of investment for each partner. A invested ₹520,000 for 12 months.
• Calculate B's investment duration. Since B joined after 8 months in a year-long business, B's money was invested for 12 - 8 = 4 months.
• Recall the fundamental formula for partnerships: The ratio of profits is equal to the ratio of the product of capital and time for each partner.
• Set up the proportion: (Profit A / Profit B) = (Capital A × Time A) / (Capital B × Time B).
• Substitute the given values: 8/2 = (520,000 × 12) / (Capital B × 4).
• Simplify the ratio 8/2 to 4/1 to make the calculation easier.

Concept Tested & Keywords

• Concept Tested: Partnership and Profit Sharing
• Stem keywords: business, capital, joined, profit, shared, ratio, invest
• Lead-in keywords: How much

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