Calculating Business Profits After Charity Contributions

In the business world, accurately determining the profit distribution and accounting for charitable donations is a common task. This article will walk you through the steps of calculating total profits after a certain percentage is set aside for charity. Let's explore a specific example involving A and B investing in a business in the ratio 3:2.

Introduction to the Problem

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, what is the total profit?

Step-by-Step Calculation

To solve this problem, we need to follow a few key steps. First, let's define the total profit as ( P ).

The profit after charity deduction will be: [ 100% - 5% 95% text{ of the total profit} ]

This means the remaining profit to be distributed between A and B is: [ frac{95}{100}P 0.95P ]

A's share in the profit is given by the ratio 3:2. Therefore, A's share is: [ frac{3}{5} times 0.95P ]

We know A's share is Rs. 855. So we can set up the equation:

[ frac{3}{5} times 0.95P 855 ]

Solving for ( P ): [ frac{3 times 0.95P}{5} 855 ]

[ frac{2.85P}{5} 855 ]

[ 2.85P 4275 ]

[ P frac{4275}{2.85} ]

[ P 1500 ]

Thus, the total profit is Rs. 1500.

Verification with Different Total Profits

To ensure the accuracy of our solution, we can verify using a total profit of 1000 (ignoring the charity contribution for a moment): [ text{Remaining profit} 95% text{ of 1000} 950 ]

A’s share (using the same 3:2 ratio): [ frac{3}{5} times 950 570 ]

Again, A's share is Rs. 570, which is less than Rs. 855. Therefore, the total profit must be scaled up:

[ text{Required total profit} frac{1500}{1.5} 1500 ]

Verification with 1000 profit shows that the formula holds true, confirming our solution.

Conclusion

In conclusion, by understanding the distribution ratios and the impact of charity contributions, we can accurately calculate the total profit in a business scenario. This method is crucial for managing investments and ensuring fair distribution of profits. If you need further assistance with similar problems or calculations, feel free to ask.

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