t answerP is a working and Q is a Sleeping partner in a business. P invested Rs. 5000 and Q invests Rs. 4000. P receives 2/11 of the profit for managing and the rest being divided in proportion to their capital. If P receives a total profit of Rs. 2800. Find the total profit.
Question
t answerP is a working and Q is a Sleeping partner in a business. P invested Rs. 5000 and Q invests Rs. 4000. P receives 2/11 of the profit for managing and the rest being divided in proportion to their capital. If P receives a total profit of Rs. 2800. Find the total profit.
Solution
Sure, let's solve this step by step:
Step 1: We know that P receives 2/11 of the profit for managing the business. So, the remaining profit that is divided between P and Q is 1 - 2/11 = 9/11 of the total profit.
Step 2: This remaining profit is divided in proportion to their capital. The ratio of their capital is 5000:4000 or 5:4.
Step 3: We know that P receives a total profit of Rs. 2800. This includes the profit for managing the business and the profit from the capital investment.
Step 4: Let's denote the total profit as X. So, P's share of the profit is (2/11)X + (5/9) * (9/11)X = 2800.
Step 5: Simplifying the equation, we get (2/11)X + (5/11)X = 2800, which simplifies to (7/11)X = 2800.
Step 6: Solving for X, we get X = 2800 * (11/7) = Rs. 4400.
So, the total profit is Rs. 4400.
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