An index number is a statistical measure that captures the relative change in a variable — price, quantity, value — from one period (the base year) to another (the current year). The base year is always assigned the value 100. Everything in the current year is expressed relative to that benchmark.
Think of it like a ruler where the base year marks 0 cm. If prices rise 25% by the current year, the index reads 125. If they double, it reads 200. The actual rupee values don't matter — only the ratio does.
Here's a concrete analogy. Suppose you're tracking the cost of a monthly grocery basket. In 2015, it cost ₹2,000. In 2023, the same basket costs ₹3,500. The index for 2023 (base 2015 = 100) is:
(3500 / 2000) × 100 = 175
This tells you grocery prices are 75% higher than in 2015 — and this interpretation is the one SSC CGL tests repeatedly. An index of 175 does not mean a 175% rise. It means a 75% rise above base.
Index numbers are used by governments and economists for three main purposes: tracking inflation (CPI, WPI), adjusting wages and contracts in real terms, and comparing economic performance across time or geography. For the CGL exam, the focus is almost entirely on the calculation methods and the properties that distinguish them.
The vocabulary you need to own before moving on:
(P₁ / P₀) × 100 for a single commodity.For a single commodity, the price relative is the most fundamental calculation:
Price Relative = (P₁ / P₀) × 100
If P₀ = ₹80 and P₁ = ₹100, the price relative = (100/80) × 100 = 125. Straightforward. Every composite index is ultimately built on this.
When you have multiple commodities and no weights:
Simple Aggregate Price Index = (ΣP₁ / ΣP₀) × 100
This is the most basic composite index. Its flaw: a high-priced commodity dominates the index regardless of how much of it people actually consume. A luxury item and a staple get equal treatment. This is why weighted indices exist.
L = (ΣP₁Q₀ / ΣP₀Q₀) × 100
Here the weights are base year quantities (Q₀). The logic is: you price the base-year consumption basket at both base-year and current-year prices, then compare.
Practical implication: Because Q₀ is fixed, Laspeyres is easy to compute continuously — you don't need fresh quantity data every year. This is why most official inflation statistics historically used Laspeyres-type formulas.
Bias: Laspeyres tends to overestimate inflation. Consumers substitute cheaper goods as prices rise, but Q₀ weights don't reflect this substitution. So Laspeyres assumes people still buy the old, now-expensive basket.
P = (ΣP₁Q₁ / ΣP₀Q₁) × 100
Here the weights are current year quantities (Q₁). You ask: how much does today's actual consumption basket cost relative to what it would have cost in the base year?
Bias: Paasche tends to underestimate inflation. Because it uses current-year quantities, it already reflects substitution toward cheaper goods — it implicitly credits consumers with more adjustment than may have happened.
Data requirement: Paasche needs fresh quantity data every period, making it more expensive to compute. This is why it's less common in practice despite its theoretical appeal.
F = √(L × P)
Fisher's index is the geometric mean of Laspeyres and Paasche. It's called "Ideal" because it satisfies two important statistical tests:
Time Reversal Test: If you swap the base year and current year, the product of the two indices should equal 1 (or 100 × 100 = 10000 before taking square root). Fisher's passes. Laspeyres and Paasche individually fail this test.
Factor Reversal Test: The product of the price index and the quantity index should equal the value index (ΣP₁Q₁ / ΣP₀Q₀) × 100. Fisher's passes. Most others fail.
When you see "Ideal index number" in any question, the answer is Fisher's. No exceptions.
Calculation pattern for CGL: Given L and P, compute √(L × P). You'll almost always get a clean square root or one that resolves to two decimal places.
ME = [Σ(Q₀ + Q₁)P₁ / Σ(Q₀ + Q₁)P₀] × 100
This uses the average of base-year and current-year quantities as weights. It partially corrects both biases but fails the Factor Reversal Test. CGL rarely asks for its calculation — mostly tested as a conceptual identifier.
Everything above applies symmetrically to quantities. Swap P and Q in all formulas:
(ΣQ₁P₀ / ΣQ₀P₀) × 100(ΣQ₁P₁ / ΣQ₀P₁) × 100√(Laspeyres_Q × Paasche_Q)| Feature | CPI | WPI | |---|---|---| | Measures | Retail prices paid by consumers | Wholesale (bulk trade) prices | | Published by | National Statistical Office (NSO) | Office of Economic Adviser, Ministry of Commerce | | Base year (current) | 2012 | 2011–12 | | Used for | Monetary policy (RBI), wage adjustment | Industrial inflation tracking |
The CPI is compiled and published by the NSO under MoSPI. The RBI uses CPI data for inflation targeting but does not publish it — a distinction CGL has tested directly.
If index = 250, base = 100:
The percentage rise = Index value − 100. This is the single most common trap in CGL index number questions.
To remember which index uses which weights: Laspeyres → Last year (base year) quantities. Paasche → Present year (current year) quantities. The first letter of the economist's name maps to the year of the weights. Standard method: recall from scratch takes 20-30 seconds. BLOB pattern: 3 seconds.
Fisher's Ideal = √(Laspeyres × Paasche). When you see L and P given numerically, multiply them first, then take the square root. Look for perfect squares or near-perfect squares. Example: L = 144, P = 125. Product = 18000 = 900 × 20. √18000 = 30√20 = 30 × 4.472 = 134.16. Standard method (decimal expansion from scratch): 45 seconds. Spotting 900 × 20 factor: 15 seconds.
Index of 250 does NOT mean 250% rise. It means (250 − 100) = 150% rise. Index of 175 means 75% rise. Index of 80 means a 20% fall. Apply this rule before reading the options — you will immediately eliminate 2-3 wrong choices. Eliminates the most common distractor in 3 seconds flat versus re-reading the question twice.
For price relative = (P₁/P₀) × 100, convert to a fraction first. P₀ = 120, P₁ = 180: recognize 180/120 = 3/2 = 1.5. Index = 150. P₀ = 80, P₁ = 100: 100/80 = 5/4 = 1.25. Index = 125. Reducing to simple fractions before multiplying by 100 is faster than long division. 4-step long division: 20 seconds. Fraction recognition: 5 seconds.
In MCQs about which index satisfies Time Reversal Test AND Factor Reversal Test, the answer is always Fisher's. If the question asks which satisfies only Time Reversal Test, Fisher's still works (along with some others). But "both tests" → Fisher's, with no need to evaluate other options. Eliminates all distractors in under 3 seconds.
In the exam hall, here is how to route each index-number question in under 5 seconds:
Step 1 — Identify the question type:
Step 2 — Trap check before computing:
Step 3 — Verify with order-of-magnitude sense: If prices rose moderately, the index should be between 100 and 200. If it's 1500 or 0.5, you made an error — likely forgot to multiply by 100 or divided the wrong way.
Why this question: Tests the most fundamental index calculation — price relative for a single commodity.
Solving path: Identify P₀ = 80, P₁ = 100. Apply (P₁/P₀) × 100 = (100/80) × 100. Simplify 100/80 = 5/4 = 1.25. Multiply by 100 = 125. Match to option D.
Why this question: Pure conceptual — "Ideal" index number is a favourite CGL identifier question.
Solving path: The word "Ideal" uniquely identifies Fisher's index. It satisfies both Time Reversal Test and Factor Reversal Test, which no other standard formula does. Direct pick — 5 seconds.
Why this question: Another price relative drill, slightly different numbers to reinforce the pattern.
Solving path: P₀ = 120, P₁ = 180. Fraction = 180/120 = 3/2. Index = (3/2) × 100 = 150. Option B.
Why this question: Tests Fisher's calculation from given L and P — the most common composite-index question type.
Solving path: L = 148, P = 145. Product = 148 × 145 = 21460. √21460 ≈ 146.49 ≈ 146.50. To estimate: 146² = 21316, 147² = 21609. 21460 is between them, closer to 146.5. Option A.
Why this question: Static GK about CPI publisher — directly tested, frequently confused with RBI.
Solving path: CPI is compiled and published by NSO under MoSPI. RBI uses CPI data for monetary policy but is not the publisher. Eliminate A (RBI), C (NITI Aayog), D (Ministry of Finance). Answer: B.
Why this question: Tests interpretation of index values — the "150% higher vs 250% higher" trap.
Solving path: Index = 250, base = 100. Rise = 250 − 100 = 150 points. Percentage rise above base = 150%. Option A is correct. Option D (250% higher) is the classic distractor — it confuses the index value with the percentage rise. Option B (50% higher) would correspond to an index of 150.
Why this question: Tests modification of Simple Aggregate Index when base-year prices change.
Solving path: Original: ΣP₁ = 360, ΣP₀ = 240. Index = (360/240) × 100 = 150 (confirmed). 6 commodities, each base-year price rises by ₹10: new ΣP₀ = 240 + (6 × 10) = 300. Current-year prices unchanged: ΣP₁ = 360. New index = (360/300) × 100 = 120. Option D.
Why this question: Fisher's calculation with messier numbers — tests whether you can factor large products.
Solving path: L = 144, P = 125. Product = 144 × 125 = 18000. Factor: 18000 = 900 × 20. √18000 = √900 × √20 = 30 × √20. √20 = √(4 × 5) = 2√5 ≈ 2 × 2.2361 = 4.4721. Answer ≈ 30 × 4.4721 = 134.16. Option A.
Confusing percentage rise with index value. An index of 250 means a 150% rise, not a 250% rise. Subtract 100 from the index to get the percentage increase. This trap appears in nearly every CGL paper.
Swapping Laspeyres and Paasche weights. Laspeyres uses base-year quantities (Q₀); Paasche uses current-year quantities (Q₁). Getting this backwards gives you the wrong formula entirely. Use the BLOB pattern: L = Last year quantities.
Attributing CPI publication to RBI. The RBI uses CPI data to set monetary policy. NSO (under MoSPI) actually publishes it. These are different roles, and CGL has tested this distinction explicitly.
Forgetting to multiply by 100. Price relative = (P₁/P₀) × 100, not just P₁/P₀. An answer of 1.25 instead of 125 means you left out the ×100 step. Always carry the ×100 through your working.
Fisher's as arithmetic mean instead of geometric mean. Fisher's Ideal = √(L × P), not (L + P)/2. The arithmetic mean of 148 and 145 is 146.5, which coincidentally looks close to the geometric mean here, but for other values the difference will cost you marks.
Misidentifying which tests each index satisfies. Laspeyres fails both the Time Reversal Test and Factor Reversal Test. Paasche also fails both. Fisher's is the only standard index that satisfies both. If a question mentions "satisfies both tests," Fisher's is the answer without analysis.