Question:
Raj and Sanjay are partners in a business firm. Raj puts in Rs. 5000 and Sanjay put in Rs. 6000. Raj receives 12.5% of the profit for managing the business and the balance is divided in the ratio of their capitals. If the total profit is Rs. 880, find Raj's total share.
Raj and Sanjay are partners in a business firm. Raj puts in Rs. 5000 and Sanjay put in Rs. 6000. Raj receives 12.5% of the profit for managing the business and the balance is divided in the ratio of their capitals. If the total profit is Rs. 880, find Raj's total share.
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Always handle the flat percentage distributions (like management fees or salaries) first, and then apply the capital ratio only to the leftover balance profit.
Updated On: Jul 24, 2026
- INR 470
- INR 465
- INR 460
- INR 455
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
In partnership businesses, profits are distributed based on capital investment ratios, but additional compensations (such as salary or management fees) are deducted from the total profit before distributing the remainder.
Key Formula or Approach:
1. Calculate Raj's management share of the profit:
\[ \text{Management Share} = \text{Total Profit} \times \text{Management Percentage} \]
2. Find the remaining balance profit to be divided among partners:
\[ \text{Balance Profit} = \text{Total Profit} - \text{Management Share} \]
3. Determine the capital investment ratio between Raj and Sanjay:
\[ \text{Ratio} = \text{Capital of Raj} : \text{Capital of Sanjay} \]
4. Distribute the balance profit based on the capital ratio and sum Raj's shares.
Step 2: Detailed Explanation:
Let us perform the calculations step-by-step:
- Total Profit = Rs. 880
- Raj's management share = \(12.5\%\) of Rs. 880:
\[ \text{Management Share} = 880 \times 0.125 = \text{Rs. } 110 \]
- Remaining balance profit to be distributed:
\[ \text{Balance Profit} = 880 - 110 = \text{Rs. } 770 \]
- Ratio of capital investments of Raj and Sanjay:
\[ \text{Ratio} = 5000 : 6000 = 5 : 6 \]
- Raj's share from the remaining balance profit:
\[ \text{Raj's Share from Balance} = 770 \times \frac{5}{5+6} = 770 \times \frac{5}{11} \]
\[ \text{Raj's Share from Balance} = 70 \times 5 = \text{Rs. } 350 \]
- Raj's total earning = Management Share + Capital Share:
\[ \text{Raj's Total Share} = 110 + 350 = \text{Rs. } 460 \]
Step 3: Final Answer:
Raj's total share of the profit is INR 460 (Option C).
In partnership businesses, profits are distributed based on capital investment ratios, but additional compensations (such as salary or management fees) are deducted from the total profit before distributing the remainder.
Key Formula or Approach:
1. Calculate Raj's management share of the profit:
\[ \text{Management Share} = \text{Total Profit} \times \text{Management Percentage} \]
2. Find the remaining balance profit to be divided among partners:
\[ \text{Balance Profit} = \text{Total Profit} - \text{Management Share} \]
3. Determine the capital investment ratio between Raj and Sanjay:
\[ \text{Ratio} = \text{Capital of Raj} : \text{Capital of Sanjay} \]
4. Distribute the balance profit based on the capital ratio and sum Raj's shares.
Step 2: Detailed Explanation:
Let us perform the calculations step-by-step:
- Total Profit = Rs. 880
- Raj's management share = \(12.5\%\) of Rs. 880:
\[ \text{Management Share} = 880 \times 0.125 = \text{Rs. } 110 \]
- Remaining balance profit to be distributed:
\[ \text{Balance Profit} = 880 - 110 = \text{Rs. } 770 \]
- Ratio of capital investments of Raj and Sanjay:
\[ \text{Ratio} = 5000 : 6000 = 5 : 6 \]
- Raj's share from the remaining balance profit:
\[ \text{Raj's Share from Balance} = 770 \times \frac{5}{5+6} = 770 \times \frac{5}{11} \]
\[ \text{Raj's Share from Balance} = 70 \times 5 = \text{Rs. } 350 \]
- Raj's total earning = Management Share + Capital Share:
\[ \text{Raj's Total Share} = 110 + 350 = \text{Rs. } 460 \]
Step 3: Final Answer:
Raj's total share of the profit is INR 460 (Option C).
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