A started a business with a capital of ₹922000. After 2 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 6 : 5. How much (in ₹) did B invest?

Appeared in: DSSSB 14 August 2024

Explanation

The core principle of partnership problems is that profit is distributed in proportion to the product of the capital invested and the duration of the investment.
For Partner A, the investment product is ₹922,000 × 12 months.
For Partner B, who joined after 2 months, the investment duration is 10 months. The investment product is B's Capital (let's call it 'x') × 10 months.
The ratio of their profits (6:5) is equal to the ratio of their investment products: (922,000 × 12) / (x × 10) = 6 / 5.
Solving this equation for 'x' reveals that B's investment is ₹922,000.

Option B: This value is incorrect. It may result from a miscalculation, such as an error in multiplication or division when solving for B's capital.
Option C: This value is incorrect. It could arise from incorrectly calculating B's investment period, for example, using 11 months instead of 10.
Option D: This value is incorrect. This might be the result of incorrectly setting up the initial ratio equation.

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 general quantitative aptitude, a skill required for various competitive examinations.
Understanding ratios and proportions is a fundamental mathematical skill applicable in various fields, including calculating dosages or interpreting financial reports.
What if B had joined after 6 months? In that case, B's investment period would be 6 months. The equation would be (922,000 × 12) / (x × 6) = 6 / 5, which would result in a different investment amount for B (x = ₹1,844,000).

How to Approach the Question

First, identify the key information provided: A's investment, the time B joins, and the final profit-sharing ratio.
Recognize that this is a partnership problem where profits are shared based on the product of capital and time.
Define the unknown variable, which is B's investment capital (let's denote it as 'x').
Calculate the investment period for each partner. A's is 12 months, and B's is 12 - 2 = 10 months.
Set up the proportion: (A's Capital × A's Time) / (B's Capital × B's Time) = A's Profit Share / B's Profit Share.
Substitute the known values into the equation: (922,000 × 12) / (x × 10) = 6 / 5.

Concept Tested & Keywords

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Practise the full DSSSB 14 August 2024

Attempt every question from this paper in a timed mock, then review the full solution for each one.