Ajay began a business with Rs. 10500 and is joined afterwards by vijay with Rs. 18000, after how many months vijay join, if the profit at the end of year is equal?

1. A

   5 months

2. B

   15 months

3. C

   10 months

4. D

   12

Appeared in: ESIC Nursing Officer 2016 (shift-1)

Explanation

• The fundamental principle of partnership is that profit is shared in the ratio of the product of the investment amount and the time period for which it was invested.
• Since the profits for Ajay and Vijay are equal, the product of their respective investments and time periods must also be equal.
• Ajay's investment is for the full 12 months. Let the time for Vijay's investment be 'x' months. The equation is: 10,500 × 12 = 18,000 × x.
• Solving this equation gives x = 7 months. This is the duration for which Vijay's money was in the business.
• The question asks for the time after which Vijay joined. This is calculated by subtracting his investment period from the total period: 12 months - 7 months = 5 months.

Why Other Options Were Wrong

• Option B: This is incorrect because the total duration of the business is only one year (12 months). It's impossible for Vijay to have joined after 15 months.
• Option C: If Vijay joined after 10 months, he would have invested for only 2 months (12 - 10). His profit share would be (18000 × 2) = 36000, which is far less than Ajay's (10500 × 12) = 126000.
• Option D: This value represents the total time Ajay was in the business. Some might mistakenly choose this, or confuse it with the time Vijay joined. If Vijay joined after 12 months, he would not have invested at all.

Related Visual

• Visual 1: Flowchart: A flowchart illustrating the step-by-step calculation: 1. Write down investments and time for Ajay. 2. Set up the equation for equal profit (10500 * 12 = 18000 * x). 3. Solve for x (Vijay's investment time). 4. Calculate joining time (12 - x). 5. Final Answer.

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 area that is part of many nursing entrance and recruitment examinations.
• Strong analytical and problem-solving skills are essential for nurses for tasks like medication dosage calculation, interpreting lab results, and managing patient data.
• What if Vijay's investment was Rs. 21,000? Then 10,500 × 12 = 21,000 × x, which gives x = 6 months. In that case, Vijay would have joined after 12 - 6 = 6 months.

How to Approach the Question

• First, identify the key information: the investment amounts for both partners (Ajay: 10,500; Vijay: 18,000) and the total time frame (1 year or 12 months).
• Recognize the core principle: In a partnership, the profit is divided in the ratio of the product of 'Investment' and 'Time'.
• Note the critical condition given in the question: 'the profit at the end of year is equal'. This means (Ajay's Investment × Ajay's Time) = (Vijay's Investment × Vijay's Time).
• Set up the equation: 10,500 × 12 = 18,000 × T_vijay.
• Solve for T_vijay, which is the duration Vijay's money was in the business.
• Finally, re-read the question carefully. It asks 'after how many months vijay join', not 'for how many months did vijay invest'. Subtract the value you found from 12 to get the final answer.

Concept Tested & Keywords

• Concept Tested: Partnership and Profit Sharing
• Stem keywords: business, joined afterwards, profit, end of year, equal
• Lead-in keywords: after how many months

Question ID

QY6igMkT1bllc2sg0W79UT

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