Home Class 11 Applied Maths Chapter 14: Tax and Utility Bills Exercise 14.2: Goods and Services Tax (GST)
Chapter 14 • Unit VI

Exercise 14.2: Goods and Services Tax (GST)

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

Comprehensive Concepts & Principles: Goods and Services Tax (GST)

Goods and Services Tax (GST) is a comprehensive, multi-stage, destination-based indirect consumption tax levied on the manufacture, sale, and consumption of goods and services throughout India. In CBSE Class 11 Applied Mathematics, GST applications provide practical commercial training in percentage markups, multi-tiered supply chains, value addition, and Input Tax Credit (ITC) balance accounting.

Key GST Architectural Components:
  • Intra-State Supply: When the location of the supplier and the place of supply are within the same state or union territory. Tax is split equally:
    $$\text{CGST Rate} = \text{SGST Rate} = \frac{1}{2} \times \text{Total GST Rate}$$
  • Inter-State Supply: When the location of the supplier and the place of supply are in different states/UTs, or in cases of import/export. Integrated GST (IGST) is levied at the full rate: $\text{IGST} = \text{CGST} + \text{SGST}$.
  • Input Tax Credit (ITC): The tax paid by a registered dealer on purchases of business inputs. Dealers can deduct Input GST from Output GST collected on sales, remitting only the net tax to the government:
    $$\text{Net GST Payable} = \text{Output GST (on Sales)} - \text{Input GST (ITC on Purchases)}$$
  • Taxable Value (Selling Price): GST is ALWAYS computed on the net discounted price:
    $$\text{Taxable Value} = \text{List Price (MRP)} - \text{Trade Discount}$$
  • Invoice Total: $\text{Total Invoice Amount} = \text{Taxable Value} + \text{CGST} + \text{SGST}$ (or $+\text{IGST}$).

Mathematical Framework & Invoicing Formulations

GST computations follow exact linear commercial percentage relationships across transaction stages:

Intra-State Invoicing Equations

  • $\text{Taxable Value } V = \text{List Price} \times (1 - d)$, where $d$ is discount rate.
  • $\text{CGST} = V \times \frac{r}{200}$
  • $\text{SGST} = V \times \frac{r}{200}$
  • $\text{Total Amount} = V \times \left(1 + \frac{r}{100}\right)$

Inter-State Invoicing Equations

  • $\text{Taxable Value } V = \text{List Price} \times (1 - d)$
  • $\text{IGST} = V \times \frac{r}{100}$
  • $\text{Total Amount} = V + \text{IGST} = V \times \left(1 + \frac{r}{100}\right)$
  • $\text{Net IGST Payable} = \text{Output IGST} - \text{Input ITC}$

Worked Benchmark Examples

Example 1 (Intra-State Retail Sale with Discount):

A laptop has a marked price of ₹60,000. A dealer in Mumbai sells it to a consumer in Pune at a discount of 10%. If GST is 18%, calculate: (i) Taxable Value, (ii) CGST and SGST, (iii) Total bill amount paid by the consumer.

Show Step-by-Step Solution

Step 1: Compute Taxable Value:
Discount = $10\% \text{ of } 60,000 = ₹6,000$.
$\text{Taxable Value} = 60,000 - 6,000 = \mathbf{₹54,000}$.

Step 2: Compute CGST & SGST (Intra-State Supply within Maharashtra):
Since both Mumbai and Pune are in Maharashtra, supply is Intra-State.
GST rate = $18\% \implies \text{CGST} = 9\%$, $\text{SGST} = 9\%$.
$\text{CGST} = 9\% \text{ of } 54,000 = 0.09 \times 54,000 = \mathbf{₹4,860}$.
$\text{SGST} = 9\% \text{ of } 54,000 = 0.09 \times 54,000 = \mathbf{₹4,860}$.

Step 3: Total Bill Amount:
$\text{Total Amount} = 54,000 + 4,860 + 4,860 = \mathbf{₹63,720}$.

Example 2 (Input Tax Credit Across Supply Chain):

A manufacturer sells goods to a wholesaler for ₹50,000. The wholesaler sells them to a retailer at a profit of ₹10,000. The retailer sells to the end consumer at a profit of ₹8,000. If GST rate is 12% and all transactions are intra-state, calculate the net tax paid by the wholesaler and the total tax collected by the government.

Show Step-by-Step Solution

1. Wholesaler Stage:
• Purchase price = ₹50,000. Input GST paid = $12\% \text{ of } 50,000 = ₹6,000$ (Input Credit).
• Selling price to retailer = $50,000 + 10,000 = ₹60,000$.
• Output GST collected = $12\% \text{ of } 60,000 = ₹7,200$.
• Net GST paid by Wholesaler = $\text{Output GST} - \text{Input GST} = 7,200 - 6,000 = \mathbf{₹1,200}$ (CGST ₹600 + SGST ₹600).

2. Retailer Stage:
• Selling price to consumer = $60,000 + 8,000 = ₹68,000$.
• Output GST collected = $12\% \text{ of } 68,000 = ₹8,160$.
• Net GST paid by Retailer = $8,160 - 7,200 = \mathbf{₹960}$ (CGST ₹480 + SGST ₹480).

3. Total Government Revenue:
Total GST = Manufacturer (₹6,000) + Wholesaler (₹1,200) + Retailer (₹960) = $\mathbf{₹8,160}$.
Note: Total tax collected matches exactly $12\%$ of final retail price ($12\% \text{ of } ₹68,000 = ₹8,160$).

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