A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:

Appeared in: ISRO- 2016

Explanation

The core of the problem is to understand that the partners' shares are calculated from the profit remaining after the charity deduction, not from the total profit.
First, calculate the portion of profit available for distribution: 100% - 5% (charity) = 95% of the total profit.
A's share is 3 parts out of a total of 5 (3+2), so A receives 3/5 of the 95% distributable profit.
The equation is set up as: (3/5) * (95% of Total Profit) = Rs. 855.
Solving this equation (0.6 * 0.95 * Total Profit = 855) gives the Total Profit as Rs. 1500.

Option A: This value represents the distributable profit, which is the amount remaining after the 5% charity donation has been deducted from the total profit (Rs. 1500 * 0.95 = Rs. 1425). The question asks for the total profit before any deductions.
Option C: This value is the result of a calculation error. It does not correspond to any logical step in the problem's solution. Such errors can occur by misapplying the percentages or ratios.
Option D: This is another incorrect value likely derived from a calculation mistake. A possible error could be incorrectly reversing the operations, for example, by adding the 5% charity amount to an intermediate sum instead of calculating it from the total.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Profit and Loss Sharing in Partnerships as background academic context rather than a clinical decision trigger.
This is a quantitative aptitude question that tests foundational mathematical skills in percentages and ratios.
These skills are essential for various competitive exams and are not directly related to clinical nursing practice.
What if A's share was Rs. 950? Following the same logic, P = 950 / 0.57, which would result in a total profit of approximately Rs. 1666.67.

How to Approach the Question

First, identify all the components of the problem: the investment ratio (3:2), the fixed deduction (5% for charity), and the known outcome (A's share = Rs. 855).
Define an unknown variable for the value you need to find, which is the 'Total Profit' (let's call it P).
Work backward from the known outcome. Before calculating A's share, the charity amount was deducted. Calculate the profit pool that A's share was drawn from (Total Profit - 5% Charity = 95% of Total Profit).
Set up an algebraic equation: A's portion of the ratio (3/5) multiplied by the distributable profit pool (0.95 * P) equals A's known share (Rs. 855).
Solve the equation for P: (3/5) * 0.95 * P = 855.
Finally, verify your answer by plugging the calculated total profit back into the problem to see if it yields A's share of Rs. 855.

Concept Tested & Keywords

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Practise the full ISRO- 2016

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