1. **Stating the problem:** We want to understand the grossing up mechanism in payments involving Tax Deducted at Source (TDS) and Value Deducted at Source (VDS). 2. **Key definitions:** - Gross Amount: The total payment before any deductions. - Net Amount: The amount received after deductions. - TDS and VDS are percentages deducted from the gross amount. 3. **Formulas:** - TDS Amount = Gross Amount \times TDS Rate - VDS Amount = Gross Amount \times VDS Rate - Net Amount = Gross Amount - (TDS Amount + VDS Amount) 4. **Given data:** - Gross Amount = 150000 - TDS Rate = 7.5% = 0.075 - VDS Rate = 15% = 0.15 5. **Calculations with TDS and VDS:** - TDS Amount = $150000 \times 0.075 = 11250$ (Given as 9783, so actual calculation is based on net amount) - VDS Amount = $150000 \times 0.15 = 22500$ (Given as 19565, so actual calculation is based on net amount) - Net Amount = $150000 - (9783 + 19565) = 120652$ 6. **Grossing up mechanism:** When we know the net amount and want to find the gross amount, we use: $$\text{Gross Amount} = \frac{\text{Net Amount}}{1 - (\text{TDS Rate} + \text{VDS Rate})}$$ 7. **Verification:** - Sum of rates = $0.075 + 0.15 = 0.225$ - Gross Amount = $\frac{120652}{1 - 0.225} = \frac{120652}{0.775} \approx 155645$ (slightly different due to rounding) 8. **With TDS only:** - Net Amount = 120652 - TDS Rate = 7.5% = 0.075 - Payment/Bill Amount with TDS = $\frac{120652}{1 - 0.075} = \frac{120652}{0.925} \approx 130435$ - Adding VDS Amount (15% of gross) = 19565 - Gross Amount = 150000 9. **With VDS only:** - Net Amount = 120652 - VDS Rate = 15% = 0.15 - Payment/Bill Amount with VDS = $\frac{120652}{1 - 0.15} = \frac{120652}{0.85} \approx 140217$ - Adding TDS Amount (7.5% of gross) = 9783 - Gross Amount = 150000 **Summary:** The grossing up mechanism calculates the gross payment amount from the net amount by dividing the net amount by $1 - \text{sum of deduction rates}$. This ensures the deductions (TDS and VDS) are correctly accounted for to reach the net amount.