A is a working and B is sleeping partners in a business. A puts in Rs. 5000 and B puts in Rs.6000. A receives 25/2% of the profit for managing the business and the rest is divided in proportion to their capital. What does each get out of a profit of Rs. 880?

Answer

To solve the problem step by step, we will follow the instructions provided in the video transcript.

### Step 1: Calculate A's share of the profit for managing the business.
A receives 25/2% of the total profit for managing the business. The total profit is Rs. 880.

\[ \text{A's share for managing} = \frac{25}{2} \% \text{ of } 880 \]

Converting the percentage to a fraction:

\[ = \frac{25}{2} \times \frac{880}{100} \]

Calculating this:

\[ = \frac{25 \times 880}{2 \times 100} = \frac{22000}{200} = 110 \]

So, A receives Rs. 110 for managing the business.

### Step 2: Calculate the remaining profit after A's share.
Now, we need to find out how much profit is left after A's share.

\[ \text{Remaining profit} = \text{Total profit} - \text{A's share for managing} \]

\[ = 880 - 110 = 770 \]

### Step 3: Determine the ratio of their investments.
A invested Rs. 5000 and B invested Rs. 6000. The ratio of their investments is:

\[ \text{Ratio of A's investment to B's investment} = 5000 : 6000 = 5 : 6 \]

### Step 4: Calculate A's and B's share from the remaining profit.
The remaining profit of Rs. 770 will be divided in the ratio of their investments (5:6).

First, we find the total parts in the ratio:

\[ \text{Total parts} = 5 + 6 = 11 \]

Now, we can calculate A's share from the remaining profit:

\[ \text{A's share from remaining profit} = \frac{5}{11} \times 770 \]

Calculating this:

\[ = \frac{5 \times 770}{11} = \frac{3850}{11} = 350 \]

Next, we calculate B's share from the remaining profit:

\[ \text{B's share from remaining profit} = \frac{6}{11} \times 770 \]

Calculating this:

\[ = \frac{6 \times 770}{11} = \frac{4620}{11} = 420 \]

### Step 5: Calculate the total amount received by A and B.
Now, we can find the total amount received by A and B.

- A's total amount = A's share for managing + A's share from remaining profit
\[ = 110 + 350 = 460 \]

- B's total amount = B's share from remaining profit
\[ = 420 \]

### Final Result:
- A receives Rs. 460
- B receives Rs. 420

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