Question 5 OR (c)
Cost-of-living index and the salary rise needed to compensate
9 marks
- Time to write
- About 18 minutes
- Topic
- Index numbers
Question
Question 5 OR (c) · 9 marksSilver Pay Solutions Pvt. Ltd., a leading FinTech company based in Pune, wants to review its employees' cost of living in order to consider a salary hike. The HR department has gathered data on the average monthly expenses of its employees under key categories for 2022 (base year) and 2025 (current year). With the information below, calculate the Cost-of-Living Index and determine the increase needed in the monthly salary to compensate for the rise in living costs for an employee who was earning ₹52,000 each month in 2022.
| Item | Average Monthly Cost (2022) | Average Monthly Cost (2025) | Weights |
|---|---|---|---|
| Housing & Rent | 14,000 | 17,500 | 3 |
| Transportation | 4,000 | 6,000 | 2 |
| Groceries and Food | 9,000 | 11,000 | 6 |
| Utilities | 2,800 | 3,600 | 2 |
| Entertainment & Misc. | 4,500 | 6,300 | 2 |
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- calculateFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Method and price relatives 3 marks 5 min
- 2 Weighted relatives and the index 3 marks 5 min
- 3 Salary needed and the increase 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 18 minutes for 9 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Method. A cost-of-living (consumer price) index measures the change in the cost of a fixed basket of a group of consumers. With weights given for each group of expenses, it is built by the weighted average of price relatives (family budget) method: R = (p₁ / p₀) × 100 for each item and CLI = ΣWR / ΣW. Here p₀ is the 2022 (base) cost and p₁ the 2025 (current) cost.
| Item | p₀ (2022, ₹) | p₁ (2025, ₹) | R = (p₁ / p₀) × 100 | W | WR |
|---|---|---|---|---|---|
| Housing & Rent | 14,000 | 17,500 | 125 | 3 | 375 |
| Transportation | 4,000 | 6,000 | 150 | 2 | 300 |
| Groceries and Food | 9,000 | 11,000 | 122.22 | 6 | 733.32 |
| Utilities | 2,800 | 3,600 | 128.57 | 2 | 257.14 |
| Entertainment & Misc. | 4,500 | 6,300 | 140 | 2 | 280 |
| Total | 15 | 1,945.46 |
CLI (2025, base 2022 = 100) = ΣWR / ΣW = 1,945.46 / 15 = 129.70.
The cost of living of the company's employees has risen by 29.70% between 2022 and 2025.
To keep the same standard of living, the 2022 salary must rise in proportion to the index:
- Salary needed in 2025 = ₹52,000 × 129.70 / 100 = ₹67,444.
- Increase needed = ₹67,444 − ₹52,000 = ₹15,444 a month (29.70% of ₹52,000). Working with the unrounded index, 129.6984, the increase is ₹15,443.
The other reading. If the weights were instead applied directly to the rupee costs (a weighted aggregative index, Σp₁W / Σp₀W × 100), the index would be 1,50,300 / 1,18,600 × 100 = 126.73 and the increase ₹13,899. The weighted average of relatives is preferred here because the items' costs are in very different sizes; weighting the relatives lets the stated weights, and not the rupee size of each item, decide each item's importance.
Where the 9 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Method and price relatives | 3 |
| 2 | Weighted relatives and the index | 3 |
| 3 | Salary needed and the increase | 3 |
| Total | 9 |
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