P 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.OptionsRs. 4400Rs. 4000Rs. 3300Rs. 5500
Question
P 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.OptionsRs. 4400Rs. 4000Rs. 3300Rs. 5500
Solution
To solve this problem, we need to follow these steps:
Step 1: We know that P receives 2/11 of the total profit for managing the business. So, the remaining profit is 1 - 2/11 = 9/11.
Step 2: This remaining profit (9/11 of the total profit) is divided between P and Q in proportion to their capital. The ratio of their capital is 5000:4000 or 5:4.
Step 3: We know that P's total profit is Rs. 2800. This includes the profit from managing the business and the profit from the capital investment.
Step 4: Let's denote the total profit as X. So, P's share for managing the business is 2/11X and P's share from the capital investment is (5/9)(9/11)X = 5/11X.
Step 5: We can set up the equation 2/11X + 5/11X = 2800. Solving this equation gives us X = Rs. 4400.
So, the total profit is Rs. 4400.
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