Question 19 of 19intermediate🔧 ApplyNumerical5 marks

The monthly expenditure (Rs.) of a family on some important items and the Goods and Services Tax (GST) rates applicable to these items is as follows: Calculate the average tax rate as far as this family is concerned.

Correct Answer

The average tax rate for this family is 9.66%.

Exercise: EXERCISES | Q: 22 | (Page Page 14)
For More Understanding

Explanation

The textbook demonstrates the calculation of average GST rate using the weighted average formula. The weights are the expenditure shares on each category of goods, and the variables are the GST rates. The total weight equals the total expenditure of the family. The solution groups items by GST rate categories and calculates the weighted contribution of each category to arrive at the average tax rate.

Solution Steps

  1. Step 1: Calculate total monthly expenditure by summing all categories. Total Expenditure = 2000 + 200 + 100 + 200 + 1000 = Rs. 3500

  2. Step 2: Calculate the weighted GST (WX) for each category by multiplying expenditure weight (w) by GST rate (x).

    • Category 1 (0% GST): 2000×02000 \times 0 = 0
    • Category 2 (5% GST): 200×0.05200 \times 0.05 = 10
    • Category 3 (12% GST): 100×0.12100 \times 0.12 = 12
    • Category 4 (18% GST): 200×0.18200 \times 0.18 = 36
    • Category 5 (28% GST): 1000×0.281000 \times 0.28 = 280

  3. Step 3: Calculate the sum of all weighted values (ΣWX). Total Weighted GST = 0 + 10 + 12 + 36 + 280 = 338

  4. Step 4: Calculate the average GST rate using the weighted average formula. Average GST Rate = ΣWX / ΣW = 338 / 3500 = 0.0966 or 9.66%

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