Calculating Total Business Profit with Charity and Partnership Sharing

This problem involves calculating the total profit of a business where partners A and B invested money, a portion of the profit goes to charity, and one partner's share is given. We need to work backwards from A's share to find the total profit before the charity deduction.

Understanding the Profit Distribution

A and B invested money in the ratio of 7 ∶ 5. The total ratio parts are \(7 + 5 = 12\). This means that any profit available for distribution among partners will be shared in this ratio, with A receiving \( \frac{7}{12} \) of the profit and B receiving \( \frac{5}{12} \).

However, the problem states that 15% of the total profit goes to charity. This means that the profit available for distribution among A and B is the remaining percentage.

• Total Profit Percentage = 100%
• Charity Percentage = 15%
• Profit available for partners = 100% - 15% = 85% of the total profit.

Calculating Profit Available for Partners

Let the Total Profit before charity be \( P\_{total} \). The amount of profit available for distribution among A and B is 85% of \( P\_{total} \).

Profit available for partners \( = 85\% \text{ of } P\_{total} = 0.85 \times P\_{total} \)

Determining A's Share of Profit

A's share is given as Rs. 5,950. This share is from the profit available for partners (after the charity deduction). Since A's investment ratio is 7 out of 12 parts, A receives \( \frac{7}{12} \) of the profit available for partners.

A's Share \( = \frac{7}{12} \times \) (Profit available for partners)

We are given A's share is Rs. 5,950. So,

\( 5950 = \frac{7}{12} \times (0.85 \times P\_{total}) \)

Calculating the Total Profit

We can first find the profit available for partners using A's share.

Let \( P\_{after} \) be the profit available for partners (after charity). We know A's share is \( \frac{7}{12} \) of \( P\_{after} \), and A's share is Rs. 5,950.

\( 5950 = \frac{7}{12} \times P\_{after} \)

To find \( P\_{after} \), we can rearrange the equation:

\( P\_{after} = 5950 \times \frac{12}{7} \)

\( P\_{after} = \frac{5950 \times 12}{7} \)

\( P\_{after} = \frac{71400}{7} \)

\( P\_{after} = 10200 \)

So, the profit available for distribution among partners (after charity) is Rs. 10,200.

Now we know that this Rs. 10,200 represents 85% of the total profit \( P\_{total} \).

\( P\_{after} = 85\% \text{ of } P\_{total} \)

\( 10200 = 0.85 \times P\_{total} \)

To find \( P\_{total} \), we divide \( P\_{after} \) by 0.85:

\( P\_{total} = \frac{10200}{0.85} \)

\( P\_{total} = \frac{10200}{85/100} \)

\( P\_{total} = \frac{10200 \times 100}{85} \)

\( P\_{total} = \frac{1020000}{85} \)

Performing the division:

\( P\_{total} = 12000 \)

Therefore, the total profit before the charity deduction was Rs. 12,000.

Conclusion

The calculated total profit is Rs. 12,000.

Revision Table: Business Profit Calculation

Additional Information: Partnership Profit Sharing

In business partnerships, profit or loss is typically shared among partners according to their investment ratio or as per the partnership agreement. When a portion of the profit is allocated for specific purposes like charity, reserves, or taxes, this amount is usually deducted from the total profit before the remaining profit is distributed among the partners.

• Profit Sharing Ratio: This ratio is often the same as the capital contribution ratio, but partners can agree on a different ratio.
• Distribution Hierarchy: Often, deductions like taxes or charity are made first from the total profit. The remaining amount is then distributed among partners based on their agreed ratio.
• Types of Profit:
  • Gross Profit: Revenue minus the cost of goods sold.
  • Net Profit: Gross Profit minus all other expenses (operating, interest, taxes). The profit shared among partners is typically derived from the net profit.
  • Distributable Profit: Net profit minus any appropriations like reserves, charity, etc. This is the amount actually shared.

Understanding the order of deductions and the basis for profit sharing is crucial in solving such partnership problems.