Home Class 11 Applied Maths Chapter 14: Tax and Utility Bills Exercise 14.1: Income Tax
Chapter 14 • Unit VI

Exercise 14.1: Income Tax

Comprehensive guide and practice questions for CBSE Class 11 Applied Mathematics curriculum (2026-27).

Comprehensive Concepts & Principles: Income Tax

Income Tax is an annual direct tax levied by the Central Government of India on the net taxable income earned by individuals, Hindu Undivided Families (HUFs), firms, and companies during a financial year. In CBSE Class 11 Applied Mathematics, income tax principles connect linear algebra, piecewise step functions, percentage calculations, and financial decision-making.

Key Tax Terms & Definitions:
  • Financial Year (FY) vs Assessment Year (AY): The Financial Year is the 12-month period (1 April to 31 March) in which income is earned. The Assessment Year is the immediately following year in which the income of the FY is evaluated and taxed. Example: Income earned in FY 2024-25 is assessed in AY 2025-26.
  • Gross Total Income (GTI): Aggregate income from all five taxable heads: (i) Income from Salaries, (ii) Income from House Property, (iii) Profits and Gains of Business/Profession, (iv) Capital Gains, and (v) Income from Other Sources.
  • Standard Deduction: A flat statutory deduction of ₹50,000 available to salaried individuals and pensioners without requiring proof of actual expense.
  • Chapter VI-A Deductions: Exemptions permissible under the Old Tax Regime, notably Section 80C (investments in PPF, EPF, ELSS, Life Insurance, NSC, up to ₹1,50,000) and Section 80D (medical insurance premiums up to ₹25,000 for self/family and ₹50,000 for senior citizen parents).
  • Taxable Income: $\text{Taxable Income} = \text{Gross Total Income} - \text{Deductions}$. Rounded off to the nearest multiple of ₹10.

Mathematical Framework & Tax Slab Formulations

Income tax follows a piecewise progressive step function where marginal increments are taxed at higher percentages.

Old Tax Regime (Individuals < 60 Years)

  • Up to ₹2,50,000: Nil
  • ₹2,50,001 to ₹5,00,000: 5% of (Income - ₹2,50,000)
  • ₹5,00,001 to ₹10,00,000: ₹12,500 + 20% of (Income - ₹5,00,000)
  • Above ₹10,00,000: ₹1,12,500 + 30% of (Income - ₹10,00,000)
  • Section 87A Rebate: Full rebate up to ₹12,500 if Taxable Income $\le$ ₹5,00,000 (Tax = Nil).

New Tax Regime (Section 115BAC)

  • Up to ₹3,00,000: Nil
  • ₹3,00,001 to ₹6,00,000: 5%
  • ₹6,00,001 to ₹9,00,000: 10%
  • ₹9,00,001 to ₹12,00,000: 15%
  • ₹12,00,001 to ₹15,00,000: 20%
  • Above ₹15,00,000: 30%
  • Section 87A Rebate: Full rebate up to ₹25,000 if Taxable Income $\le$ ₹7,00,000 (Tax = Nil).
Health & Education Cess: An additional 4% cess is computed on the total tax payable after adjusting for the Section 87A rebate: $\text{Total Tax Liability} = (\text{Tax} - \text{Rebate 87A}) \times 1.04$.

Worked Benchmark Examples

Example 1 (Salaried Individual under Old Regime):

Mr. Rajesh (age 42) has a gross salary of ₹9,20,000 in FY 2024-25. He deposits ₹1,40,000 in PPF, ₹20,000 in ELSS, and pays ₹24,000 for medical insurance (Section 80D). Calculate his total tax liability under the Old Regime.

Show Step-by-Step Solution

Step 1: Compute Total Deductions:
• Standard Deduction = ₹50,000
• Section 80C: PPF (₹1,40,000) + ELSS (₹20,000) = ₹1,60,000. Capped at maximum statutory limit = ₹1,50,000.
• Section 80D: Health insurance premium = ₹24,000 (within ₹25,000 limit).
Total Deductions = $50,000 + 1,50,000 + 24,000 = \mathbf{₹2,24,000}$.

Step 2: Compute Taxable Income:
$\text{Taxable Income} = 9,20,000 - 2,24,000 = \mathbf{₹6,96,000}$.

Step 3: Calculate Income Tax (Old Regime Slabs):
• On first ₹2,50,000: Nil
• On ₹2,50,001 to ₹5,00,000 (₹2,50,000 @ 5%): $0.05 \times 2,50,000 = ₹12,500$
• On remaining ₹1,96,000 (₹6,96,000 - ₹5,00,000) @ 20%: $0.20 \times 1,96,000 = ₹39,200$
Total Tax before Cess = $12,500 + 39,200 = \mathbf{₹51,700}$.

Step 4: Add 4% Health & Education Cess:
$\text{Cess} = 0.04 \times 51,700 = ₹2,068$.
$\text{Net Tax Payable} = 51,700 + 2,068 = \mathbf{₹53,768}$.

Example 2 (Section 87A Full Rebate Scenario):

Ms. Ananya has a taxable income of ₹4,80,000 under the Old Regime. Determine her tax payable after applying Section 87A rebate.

Show Step-by-Step Solution

Tax before rebate:
Up to ₹2,50,000: Nil
₹2,50,001 to ₹4,80,000: $5\% \text{ of } (4,80,000 - 2,50,000) = 0.05 \times 2,30,000 = ₹11,500$.

Section 87A Rebate:
Since Taxable Income $\le ₹5,00,000$, she is eligible for full rebate up to ₹12,500. Here, rebate = ₹11,500.
$\text{Net Tax Payable} = 11,500 - 11,500 = \mathbf{₹0}$ (Nil).

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