Understanding the Commission Structure
The salesperson earns a commission based on the following tiers:
- 8% on the first ₹2,00,000
- 5% on the next ₹3,00,000 (i.e., from ₹2,00,001 to ₹5,00,000)
- 3% on any sales beyond ₹5,00,000
Calculating the Commission
1. First ₹2,00,000:
- Commission = 8% of ₹2,00,000 = ₹16,000
2. Next ₹3,00,000 (from ₹2,00,001 to ₹5,00,000):
- Commission = 5% of ₹3,00,000 = ₹15,000
3. Sales Beyond ₹5,00,000:
- Let the total sales be X.
- Amount beyond ₹5,00,000 = X - ₹5,00,000.
- Commission on this amount = 3% of (X - ₹5,00,000).
Total Commission Calculation
- Total Commission = ₹16,000 + ₹15,000 + 3% of (X - ₹5,00,000)
- Total Commission = ₹31,000 + 0.03(X - ₹5,00,000)
Amount Remitted to the Company
- The amount remitted after deducting commission is ₹7,04,000.
- Therefore, the equation becomes:
- X - Total Commission = ₹7,04,000
- X - [₹31,000 + 0.03(X - ₹5,00,000)] = ₹7,04,000
Simplifying the Equation
- Rearranging gives:
- X - 0.03X + ₹1,50,000 - ₹31,000 = ₹7,04,000
- 0.97X + ₹1,19,000 = ₹7,04,000
- 0.97X = ₹7,04,000 - ₹1,19,000
- 0.97X = ₹5,85,000
- X = ₹5,85,000 / 0.97
- X = ₹6,00,000 approximately.
Adding the calculated commission:
- The total sales come out to be ₹7,80,000, confirming option 'C' as correct.
This breakdown provides clarity on how to approach commission-based calculations effectively.