hree friends A, B, and C invested in a business in the ratio of 3 : 2 : 6. After 6 months, C withdrew half of his capital. The total profit at the end of the year is Rs. 53010. What is the profit made by A?

1. A

   16740

2. B

   19740

3. C

   17740

4. D

   18740

Appeared in: AIIMS Delhi NO - 2018

Explanation

• The fundamental principle is that profit is shared in the ratio of the product of capital and the duration of investment.
• A's effective investment is 3 units for 12 months (3x12=36).
• B's effective investment is 2 units for 12 months (2x12=24).
• C's investment changes mid-year: 6 units for 6 months and 3 units for the next 6 months, making the effective investment (6x6) + (3x6) = 54.
• The profit-sharing ratio A:B:C is 36:24:54, which simplifies to 6:4:9.
• A's share is (6 / (6+4+9)) of the total profit, which is (6/19) * 53010 = 16740.

Why Other Options Were Wrong

• Option B: This value is incorrect and likely results from a calculation error, such as miscalculating the simplified ratio or the value of each part of the profit.
• Option C: This value is incorrect. It may arise from an error in calculating C's adjusted capital or a mistake during the final multiplication.
• Option D: This value is incorrect. This could be the result of incorrectly summing the ratio parts or an arithmetic mistake.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Profit sharing in a business partnership where the capital invested changes over time as background academic context rather than a clinical decision trigger.
• This question assesses general aptitude and numerical reasoning skills, which are essential for various non-clinical aspects of nursing management and administration.
• While not a direct clinical calculation, the logical thinking required is similar to what is needed for tasks like resource allocation or staff scheduling based on patient load ratios.
• What if C had added half of his capital instead of withdrawing? C's effective capital would be (6x6) + (9x6) = 36 + 54 = 90. The new ratio would be 36:24:90 (or 6:4:15), and A's profit would be (6/25) * 53010 = Rs. 12722.4.

How to Approach the Question

• First, identify the initial investment ratio for each partner (A:B:C = 3:2:6).
• Note the total time period for the profit calculation, which is one year (12 months).
• Carefully read for any changes in capital. Here, C withdraws half his capital after 6 months.
• Calculate the 'effective capital' for each partner by multiplying their capital by the time it was invested. For partners with changing capital, calculate it in parts and sum them up.
• Form a ratio of these effective capitals (A:B:C). Simplify this ratio to its lowest terms.
• Sum the parts of the simplified ratio. Divide the total profit by this sum to find the value of one part. Finally, multiply this value by the ratio part of the partner in question (A).

Concept Tested & Keywords

• Concept Tested: Profit sharing in a business partnership where the capital invested changes over time.
• Stem keywords: invested, business, ratio, capital, withdrew, profit
• Lead-in keywords: What is

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QB1lrB-TRIwOVbjjUb5eKn

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