Basics of Financial Mathematics

Step 1: Calculate Gross Total Income

| Head of Income | Amount (₹) |
|---|---|
| Income from Salary | 2,00,000 |
| Income from Capital Gains | 1,50,000 |
| Income from Other Sources | 2,50,000 |
| Gross Total Income | 6,00,000 |

Step 2: Calculate Deductions under Section 80C

| Particulars | Amount (₹) |
|---|---|
| PF Contribution | 40,000 |
| PPF Contribution | 70,000 |
| LIC Premium | 40,000 |
| Total | 1,50,000 |

Maximum deduction allowed under Section 80C = ₹1,50,000

Since total = ₹1,50,000, deduction = ₹1,50,000

Step 3: Calculate Total Taxable Income

$$\text{Total Taxable Income} = \text{Gross Total Income} - \text{Deductions under 80C}$$

$$= ₹6,00,000 - ₹1,50,000 = ₹4,50,000$$

Step 4: Calculate Income Tax (as per Old Regime slabs)

| Slab | Rate | Tax (₹) |
|---|---|---|
| Up to ₹2,50,000 | Nil | 0 |
| ₹2,50,001 – ₹5,00,000 | 5% | 5% × ₹2,00,000 = 10,000 |
| Total Tax | | 10,000 |

Step 5: Add Health & Education Cess @ 4%

$$\text{Cess} = 4\% \times ₹10,000 = ₹400$$

Step 6: Total Income Tax Liability

$$\text{Total Tax Liability} = ₹10,000 + ₹400 = \boxed{₹10,400}$$

Note: A rebate under Section 87A of ₹12,500 is available if total taxable income does not exceed ₹5,00,000. Since taxable income here is ₹4,50,000 (≤ ₹5,00,000), the rebate applies and the tax payable becomes ₹NIL (tax of ₹10,000 < rebate limit of ₹12,500).

$$\therefore \text{Income Tax Liability of Mr X} = \mathbf{₹0}$$

Step 1: Calculate Gross Total Income

| Head of Income | Amount (₹) |
|---|---|
| Income from Salary | 3,00,000 |
| Income from House Property (Rentals) | 1,50,000 |
| Income from Capital Gains | 3,00,000 |
| Income from Other Sources | 50,000 |
| Gross Total Income | 8,00,000 |

Step 2: Calculate Deductions under Section 80C

| Particulars | Amount (₹) |
|---|---|
| PF | 40,000 |
| PPF | 40,000 |
| Fixed Deposits (Tax Saving, 5-yr) | 30,000 |
| LIC Premium | 40,000 |
| Total | 1,50,000 |

Maximum deduction allowed under Section 80C = ₹1,50,000

Since total = ₹1,50,000, deduction = ₹1,50,000

Step 3: Calculate Total Taxable Income

$$\text{Total Taxable Income} = ₹8,00,000 - ₹1,50,000 = ₹6,50,000$$

Step 4: Calculate Income Tax (as per Old Regime slabs)

| Slab | Rate | Tax (₹) |
|---|---|---|
| Up to ₹2,50,000 | Nil | 0 |
| ₹2,50,001 – ₹5,00,000 | 5% | 5% × ₹2,50,000 = 12,500 |
| ₹5,00,001 – ₹6,50,000 | 20% | 20% × ₹1,50,000 = 30,000 |
| Total Tax | | 42,500 |

Step 5: Add Health & Education Cess @ 4%

$$\text{Cess} = 4\% \times ₹42,500 = ₹1,700$$

Step 6: Total Income Tax Liability

$$\text{Total Tax Liability} = ₹42,500 + ₹1,700 = \boxed{₹44,200}$$

Note: Since taxable income exceeds ₹5,00,000, rebate under Section 87A is NOT applicable.

$$\therefore \text{Income Tax Liability of Mr A} = \mathbf{₹44,200}$$

Given:
- Original cost of product = ₹2,000
- GST rate = 12%

Formula:
$$\text{GST Amount} = \frac{\text{Original Cost} \times \text{GST\%}}{100}$$

Step 1: Calculate GST Amount

$$\text{GST Amount} = \frac{₹2,000 \times 12}{100} = ₹240$$

Step 2: Calculate Net Price

$$\text{Net Price} = \text{Original Cost} + \text{GST Amount}$$

$$\text{Net Price} = ₹2,000 + ₹240 = \boxed{₹2,240}$$

$$\therefore \text{The net price of the product after adding GST is } \mathbf{₹2,240}.$$

Given:
- Service Charge = ₹40/month (build-up area ≤ 200 sq. m)
- Consumption Charges:
- 0 – 6,000 litres → NIL
- 7,001 – 20,000 litres → ₹2 per litre (for units above 6,000)
- 21,001 – 30,000 litres → ₹7 per litre (for units in this slab)
- Above 30,000 litres → ₹10 per litre (for units above 30,000)
- Sewage Charge = 50% of Consumption Charge

---

(a) Consumption = 6,000 litres

$$\text{Service Charge} = ₹40$$
$$\text{Consumption Charge} = ₹0 \text{ (NIL for 0–6000 litres)}$$
$$\text{Sewage Charge} = 50\% \times 0 = ₹0$$
$$\text{Total Bill} = ₹40 + 0 + 0 = \boxed{₹40}$$

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(b) Consumption = 10,000 litres

$$\text{Service Charge} = ₹40$$
$$\text{Consumption Charge} = (10,000 - 6,000) \times ₹2 = 4,000 \times 2 = ₹8$$

(First 6,000 litres are free; next 4,000 litres @ ₹2 each)

$$\text{Sewage Charge} = 50\% \times ₹8 = ₹4$$
$$\text{Total Bill} = ₹40 + ₹8 + ₹4 = \boxed{₹52}$$

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(c) Consumption = 20,000 litres

$$\text{Service Charge} = ₹40$$
$$\text{Consumption Charge} = (20,000 - 6,000) \times ₹2 = 14,000 \times 2 = ₹28$$

(First 6,000 litres free; next 14,000 litres @ ₹2 each)

$$\text{Sewage Charge} = 50\% \times ₹28 = ₹14$$
$$\text{Total Bill} = ₹40 + ₹28 + ₹14 = \boxed{₹82}$$

---

(d) Consumption = 21,000 litres

$$\text{Service Charge} = ₹40$$

Consumption Charge:
- First 6,000 litres → NIL
- Next 14,000 litres (6,001 to 20,000) @ ₹2 = ₹28
- Next 1,000 litres (20,001 to 21,000) @ ₹7 = ₹7

$$\text{Total Consumption Charge} = ₹28 + ₹7 = ₹35$$

$$\text{Sewage Charge} = 50\% \times ₹35 = ₹17.50$$

$$\text{Total Bill} = ₹40 + ₹35 + ₹17.50 = \boxed{₹92.50 \approx ₹93}$$

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(e) Consumption = 31,000 litres

$$\text{Service Charge} = ₹40$$

Consumption Charge:
- First 6,000 litres → NIL
- Next 14,000 litres (6,001 to 20,000) @ ₹2 = ₹28
- Next 10,000 litres (20,001 to 30,000) @ ₹7 = ₹70
- Next 1,000 litres (30,001 to 31,000) @ ₹10 = ₹10

$$\text{Total Consumption Charge} = ₹28 + ₹70 + ₹10 = ₹108$$

$$\text{Sewage Charge} = 50\% \times ₹108 = ₹54$$

$$\text{Total Bill} = ₹40 + ₹108 + ₹54 = \boxed{₹202}$$

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Summary Table:

| Consumption (litres) | Service Charge (₹) | Consumption Charge (₹) | Sewage Charge (₹) | Total Bill (₹) |
|---|---|---|---|---|
| 6,000 | 40 | 0 | 0 | 40 |
| 10,000 | 40 | 8 | 4 | 52 |
| 20,000 | 40 | 28 | 14 | 82 |
| 21,000 | 40 | 35 | 17.50 | ≈93 |
| 31,000 | 40 | 108 | 54 | 202 |