Quantitative Aptitude · Index Numbers

Methods of Constructing Index Numbers for CA Foundation

Updated 1 October 2026 · Fact-checked

An index number measures the average change in a group of prices or quantities against a base year, with the base set at 100. For unweighted methods, use the simple aggregate (Σp1 ÷ Σp0 × 100) or the simple average of price relatives (Σ(p1 ÷ p0 × 100) ÷ n).

Understand Methods of Constructing Index Numbers

An index number is a single figure that shows how a group of related items has changed over time. Prices of rice, wheat and oil all move differently. An index number squeezes these movements into one number so you can say, for example, that prices rose by 25%.

The period you compare against is the base year. Its index is always taken as 100. The period you are measuring is the current year. If the current index is 125, the group has risen 25% over the base. If it is 90, the group has fallen 10%.

Construction follows a fixed path. First decide the purpose and the items. Then choose a suitable base year, which should be a normal year without wars, floods or sharp swings. Collect prices for the base and current years. Finally choose a method and compute.

Methods split into two families. Unweighted methods treat every item as equally important. Weighted methods give more importance to items that matter more, such as quantities consumed. This page covers the unweighted ones: the simple aggregate method and the simple average of price relatives method.

A price relative is the current price as a percentage of the base price: (p1 ÷ p0) × 100. The simple aggregate method adds the prices first, then compares totals. The price relatives method compares each item first, then averages.

Key formulas to remember

Simple aggregate price index: P01 = (Σp1 ÷ Σp0) × 100; p1 = current year price, p0 = base year price. Add prices of all items first, then divide.
Price relative: Price relative = (p1 ÷ p0) × 100; Calculated separately for each item. For the base year it is 100.
Simple average of price relatives (arithmetic mean): P01 = Σ[(p1 ÷ p0) × 100] ÷ n; n = number of items. Other averages such as the geometric mean can also be used, but the arithmetic mean is the usual default.
Percentage change from index: Percentage change = Index − 100; Valid when the base index is 100. An index of 135 means a 35% rise over the base year.

How to solve Methods of Constructing Index Numbers questions

Use this routine for any question on unweighted index numbers. It keeps p0 and p1 from getting swapped.

1Read which year is the base and which is the current year. Label them p0 (base) and p1 (current).
2Note which method the question names: simple aggregate or simple average of price relatives. If none is named, check the wording and options.
3For simple aggregate, add all base prices to get Σp0 and all current prices to get Σp1.
4Divide Σp1 by Σp0 and multiply by 100.
5For price relatives, compute (p1 ÷ p0) × 100 for each item, add them, and divide by the number of items n.
6State the answer as an index number. If the question asks for the rise or fall, subtract 100.
7Check that the answer is sensible: the index should be above 100 if most prices rose, and below 100 if most fell.

Quickest way: Option elimination with a quick estimate

When to use it: Use this in the MCQ paper when the numbers are small and four options are given.

Add the base prices and the current prices mentally for the aggregate method. Do not compute each relative.
Estimate Σp1 ÷ Σp0. If totals are 200 and 250, the index is clearly 125.
Check direction: if prices rose overall, discard options below 100.
For price relatives, pick prices that give round ratios such as 2, 1.5 or 1.25 and convert them directly to 200, 150 or 125.
Look at the options. Often only one fits your estimate, so stop there.
Skip long decimal calculations if you are short on time. A wrong answer costs 0.25 marks.

Common mistakes in Methods of Constructing Index Numbers

Swapping p0 and p1 in the formula.
Students rush and put the base total in the numerator.
Fix: Write p0 = base and p1 = current at the top of the page. The current year always goes on top.
Forgetting to multiply by 100.
The division gives a ratio like 1.25, which looks like a finished answer.
Fix: An index is a percentage form. Always convert 1.25 to 125.
Averaging price relatives by dividing by the wrong number.
Students divide by Σp0 or by 100 instead of the number of items.
Fix: Divide the sum of relatives by n, the count of items.
Using the price relatives method when asked for simple aggregate, or the reverse.
Both methods use the same data and look similar.
Fix: Aggregate adds prices first. Relatives method finds ratios first. Check the method name in the question.
Treating the aggregate method as if it handles units well.
Students forget that prices in different units (per kg, per dozen) are being added.
Fix: Remember that this is a weakness of the simple aggregate method. The price relatives method does not depend on units, since each ratio is unit-free.
Reporting the index as the percentage change.
An index of 140 is read as a 140% rise.
Fix: Subtract 100 when the base is 100. An index of 140 means a 40% rise.

Worked examples

Example 1

Prices (₹ per unit) of four items are: base year 10, 20, 30, 40 and current year 15, 25, 35, 45. The simple aggregate price index is: (a) 115 (b) 120 (c) 130 (d) 150

Show the solution

Σp0 = 10 + 20 + 30 + 40 = 100.
Σp1 = 15 + 25 + 35 + 45 = 120.
Index = (120 ÷ 100) × 100 = 120.

Answer: (b) 120

Example 2

Base year prices of three items are ₹10, ₹20 and ₹40. Current year prices are ₹20, ₹30 and ₹60. The simple average of price relatives index is: (a) 150 (b) 160 (c) 166.67 (d) 180

Show the solution

Relative for item 1 = (20 ÷ 10) × 100 = 200.
Relative for item 2 = (30 ÷ 20) × 100 = 150.
Relative for item 3 = (60 ÷ 40) × 100 = 150.
Sum of relatives = 200 + 150 + 150 = 500.
Index = 500 ÷ 3 = 166.67.

Answer: (c) 166.67

Example 3

Using the same data as the previous problem, the simple aggregate index is: (a) 128.57 (b) 150 (c) 157.14 (d) 166.67

Show the solution

Σp0 = 10 + 20 + 40 = 70.
Σp1 = 20 + 30 + 60 = 110.
Index = (110 ÷ 70) × 100 = 157.14.

Answer: (c) 157.14. Note that it differs from the price relatives result of 166.67, because the two methods weigh the items differently.

Exam tips

Read the method name first. Questions often give the same data and ask for either method, so the options will include both answers.
Use round-number data to your advantage. Ratios like 2, 1.5 and 1.25 convert straight into 200, 150 and 125.
Remember the standard facts: base year index is 100, and the simple aggregate method gives equal importance to all items in effect by price size.
Theory MCQs often ask which method is unaffected by the units of measurement. The answer is the simple average of price relatives.
If a calculation needs more than about a minute, mark it, move on and return if time remains.

Practice questions from Index Numbers

Methods of Constructing Index Numbers: frequently asked questions

What is the base year in an index number?

The base year is the reference period against which all other periods are compared. Its index value is set at 100. It should be a normal year without unusual events.

What is the difference between the simple aggregate method and the price relatives method?

The aggregate method adds all prices first and then compares the two totals. The price relatives method finds each item's ratio first and then takes the average. The second method is not affected by the units in which prices are quoted.

What is the difference between simple and weighted index numbers?

Simple index numbers treat all items alike and use no weights. Weighted index numbers assign weights, usually quantities, so more important items affect the index more. Laspeyres, Paasche and Fisher are weighted methods.

Can an index number be below 100?

Yes. An index below 100 means prices have fallen compared with the base year. For example, an index of 92 shows an 8% fall.