The accountant of XYZ Corp. is entitled to a commission of 10% on net profits, after charging such commission. If the amount of commission payable for the year is Rs. 30,000, the net profit of XYZ Corp. after such commission would be:
Rs. 3,00,000
Understanding Commission Calculation Based on Net Profit After Commission
This question requires calculating the net profit after commission when the commission rate is applied to this final profit figure. The key phrase is "commission of 10% on net profits, after charging such commission". This means the commission is calculated based on the profit amount that remains *after* the commission itself has been deducted.
Defining Variables for Calculation
To solve this problem clearly, let's define the terms:
- Let $N$ represent the net profit after commission. This is the target value we need to determine.
- Let $C$ represent the commission amount payable to the accountant. We are given that $C = \text{Rs. } 30,000$.
- The commission rate is specified as $10\%$ of the net profit after commission.
Formulating the Equation for Commission
According to the problem statement, the commission ($C$) is calculated as 10% of the net profit after commission ($N$). We can write this relationship as an equation:
$C = 10\% \times N$
Converting the percentage to a decimal for calculation:
$C = 0.10 \times N$
Step-by-Step Calculation of Net Profit After Commission
We know the actual commission amount is Rs. 30,000. We can substitute this known value into our equation:
$\text{Rs. } 30,000 = 0.10 \times N$
To find the net profit after commission ($N$), we need to isolate $N$ by rearranging the equation. We can do this by dividing both sides by 0.10:
$N = \frac{\text{Rs. } 30,000}{0.10}$
Performing the division:
$N = \text{Rs. } 3,00,000$
Verification of the Result
To ensure our calculation is correct, let's check if a net profit after commission of Rs. 3,00,000 yields the given commission amount:
Commission = $10\%$ of Rs. 3,00,000
Commission = $0.10 \times \text{Rs. } 3,00,000
Commission = Rs. 30,000
This calculated commission matches the amount given in the question (Rs. 30,000), confirming that our value for the net profit after commission is accurate.
Conclusion on Net Profit After Commission
Therefore, the net profit of XYZ Corp. after charging the commission is Rs. 3,00,000.
| Item | Amount (Rs.) |
|---|---|
| Net Profit After Commission ($N$) | 3,00,000 |
| Commission ($10\%$ of $N$) | 30,000 |
| Net Profit Before Commission ($N+C$) | 3,30,000 |
The net profit after commission is Rs. 3,00,000, which corresponds to the second option.
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