Divyaraj and Ayush started a business in partnership investing 36000 Rs and 24000 Rs and after 6 month they added 4000 Rs and 6000 Rs respectively `33 1/3` % of total profit after one year they donated and Remaining profit shared in the ratio of invested capital . If Divyaraj gets 8800 Rs more profit to Ayush , then find the total profit ?

Options

A. A)78000
B. B)75000
C. C)56000
D. D)91000

Answer

To solve the problem step by step, we will break it down as follows:

### Step 1: Determine Initial Investments
Divyaraj invested Rs. 36,000 and Ayush invested Rs. 24,000.

### Step 2: Calculate Total Investment After 6 Months
After 6 months, Divyaraj added Rs. 4,000, making his total investment Rs. 40,000. Ayush added Rs. 6,000, making his total investment Rs. 30,000.

### Step 3: Calculate the Effective Capital Contribution
- Divyaraj's investment for the first 6 months: Rs. 36,000
- Divyaraj's investment for the next 6 months: Rs. 40,000
- Ayush's investment for the first 6 months: Rs. 24,000
- Ayush's investment for the next 6 months: Rs. 30,000

Now, we calculate the effective capital contribution in terms of "capital-months":
- Divyaraj:
- First 6 months: \( 36,000 \times 6 = 216,000 \)
- Next 6 months: \( 40,000 \times 6 = 240,000 \)
- Total for Divyaraj: \( 216,000 + 240,000 = 456,000 \)

- Ayush:
- First 6 months: \( 24,000 \times 6 = 144,000 \)
- Next 6 months: \( 30,000 \times 6 = 180,000 \)
- Total for Ayush: \( 144,000 + 180,000 = 324,000 \)

### Step 4: Calculate the Profit Sharing Ratio
The ratio of their effective capital contributions is:
\[ \text{Divyaraj : Ayush} = 456,000 : 324,000 \]
To simplify this ratio, we can divide both sides by 12,000:
\[ \text{Divyaraj : Ayush} = 38 : 27 \]

### Step 5: Calculate Total Profit After Donation
Let the total profit be \( P \). According to the problem, they donated \( 33 \frac{1}{3} \% \) of the total profit, which is equivalent to \( \frac{1}{3} \) of \( P \). Therefore, the remaining profit is:
\[ \text{Remaining Profit} = P - \frac{1}{3}P = \frac{2}{3}P \]

### Step 6: Share the Remaining Profit
The remaining profit of \( \frac{2}{3}P \) is shared in the ratio of 38:27. The total parts of the ratio are:
\[ 38 + 27 = 65 \text{ parts} \]

### Step 7: Calculate the Value of Each Part
Let the value of each part be \( x \). Then:
\[ \text{Divyaraj's share} = 38x \]
\[ \text{Ayush's share} = 27x \]

According to the problem, Divyaraj's profit is Rs. 8,800 more than Ayush's profit:
\[ 38x = 27x + 8800 \]
Solving for \( x \):
\[ 38x - 27x = 8800 \]
\[ 11x = 8800 \]
\[ x = 800 \]

### Step 8: Calculate Total Profit
Now, we can find the total remaining profit:
\[ \text{Remaining Profit} = 65x = 65 \times 800 = 52000 \]
Since this is \( \frac{2}{3}P \):
\[ \frac{2}{3}P = 52000 \]
To find \( P \):
\[ P = 52000 \times \frac{3}{2} = 78000 \]

### Final Answer
The total profit \( P \) is Rs. 78,000.

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