Index Numbers Worked Examples (Easy)

Q: What exactly does a price index of 125 mean?

It means the price is 125%125\%125% of its base-year value, a rise of 25%25\%25%. An index equal to 100100100 means the price is unchanged from the base year, and an index below 100100100 means it has fallen.

Q: Which price goes on the bottom of the fraction?

The base-year price P0P_0P0 is the denominator, and the price you are comparing, P1P_1P1, is the numerator: I=P1P0×100I=\frac{P_1}{P_0}\times 100I=P0P1×100. Swapping the two is the most common slip.

Q: How do I turn a percentage change into an index?

Add to or subtract from 100100100. A rise of 20%20\%20% gives 120120120; a fall of 8%8\%8% gives 929292. Then scale a price with P1=I100×P0P_1=\frac{I}{100}\times P_0P1=100I×P0.

What these examples cover

These easy Index Numbers examples build the single idea the whole chapter rests on: a price index compares a price at the time of interest with the price in a chosen base year, written as $\frac{P_1}{P_0}\times 100$ . Across the four questions you will read an index and say what it means, find a later price from an index, recover a base-year price, and turn a percentage change straight into an index.

Every number is small and clean, so you can follow each line without leaning on a calculator. Cover the solution, attempt the question in full on paper, then check line by line against our working.

Where your answer differs, find the exact step that parted from ours, that single line is usually where the real learning is.

Worked examples

Work through all four in order. Attempt each fully before you read the matching solution, and notice how one formula, $\frac{P_1}{P_0}\times 100$ , and one habit, decide the base year first, then substitute, carry every question.

Q1[3 marks]

A kilogram of rice cost RM4.00 in the year 2020 and RM5.00 in 2023. Taking 2020 as the base year, find the price index of rice for 2023 based on 2020, and state what it tells you.

Show worked solution

The price index compares the price at the time of interest with the price in the base year. Write the formula, with $P_0$ the base-year price and $P_1$ the price in the year of interest:

I=\frac{P_1}{P_0}\times 100

The base year 2020 gives $P_0=4.00$ , and the year of interest 2023 gives $P_1=5.00$ . Substitute these values:

I=\frac{5.00}{4.00}\times 100=1.25\times 100=125

Answer

The price index for 2023 based on 2020 is $125$ . Because it sits $25$ above $100$ , the price of rice rose by $25\%$ over those three years.

Q2[3 marks]

The price index of an item for 2024 based on 2021 is $120$ . If the item cost RM60 in 2021, find its price in 2024.

Show worked solution

Start from the same formula and label what is known: the index $I=120$ and the base-year price $P_0=60$ . The unknown is the later price $P_1$ .

I=\frac{P_1}{P_0}\times 100

Substitute the known values, then rearrange to make $P_1$ the subject:

120=\frac{P_1}{60}\times 100

P_1=\frac{120\times 60}{100}=\frac{7200}{100}=72

Answer

The price in 2024 is RM72. Check: $\frac{72}{60}\times 100=120$ , which matches the given index.

Q3[3 marks]

The price index of an item for 2025 based on 2020 is $140$ , and the item costs RM70 in 2025. Find its price in 2020.

Show worked solution

This time the later price is known and the base-year price $P_0$ is the unknown. Substitute the values $I=140$ and $P_1=70$ into the formula:

140=\frac{70}{P_0}\times 100

Rearrange to make $P_0$ the subject, keeping the base-year price on the denominator throughout:

P_0=\frac{70\times 100}{140}=\frac{7000}{140}=50

Answer

The price in 2020 was RM50. Check: $\frac{70}{50}\times 100=140$ , as required.

Q4[4 marks]

The price of a type of building sand rose by $15\%$ from 2022 to 2024. (a) Write down the price index for 2024 based on 2022.

(b) If the price in 2022 was RM80 per tonne, find the price in 2024.

Show worked solution

(a) A price index measures a price against a base of $100$ . An increase of $15\%$ adds $15$ to that base:

I=100+15=115

(b) Use the index to scale the base-year price up to the 2024 price, with $P_1=\frac{I}{100}\times P_0$ :

P_1=\frac{115}{100}\times 80=92

Answer

The price index is $115$ and the 2024 price is RM92. Check the percentage directly: $80\times 1.15=92$ , a rise of RM12, which is exactly $15\%$ of RM80.

Q5[2 marks]

The price indices of three items, A, B and C, for 2024 based on 2020 are $110$ , $120$ and $130$ respectively. Find the average (simple) price index of the three items.

Show worked solution

When several items are compared together with equal importance, their overall change is summarised by the simple average of the individual price indices.

\bar{I}=\frac{\sum I}{n}

There are $n=3$ items, and their indices sum to $110+120+130=360$ :

\bar{I}=\frac{360}{3}=120

Answer

The average price index of the three items is $120$ , so together they rose by $20\%$ from 2020 to 2024.

Q6[3 marks]

The price index of rice for 2023 based on 2020 is $120$ with a weight of $3$ , while the price index of sugar for the same period is $150$ with a weight of $2$ . Calculate the composite index for the two items.

Show worked solution

A composite index weighs each item's price index by its importance, using $I=\frac{\sum WI}{\sum W}$ , where $W$ is the weight and $I$ is each item's price index.

\bar{I}=\frac{\sum WI}{\sum W}

Substitute the weight and price index of each item:

\bar{I}=\frac{(3)(120)+(2)(150)}{3+2}=\frac{360+300}{5}=\frac{660}{5}=132

Answer

The composite index is $132$ , so overall the two items rose by $32\%$ from 2020 to 2023, once rice's greater weight is taken into account.

Q7[3 marks]

The price index of an item for 2022 based on 2020 is $110$ . The price index of the same item for 2024 based on 2022 is $120$ .

Find the price index of the item for 2024 based on 2020.

Show worked solution

Two indices can be chained end to end using $I_{13}=\frac{I_{12}\times I_{23}}{100}$ , where the middle year 2022 cancels out.

I_{2024/2020}=\frac{I_{2022/2020}\times I_{2024/2022}}{100}

Substitute the two given indices:

I_{2024/2020}=\frac{110\times 120}{100}=\frac{13200}{100}=132

Answer

The price index for 2024 based on 2020 is $132$ , so the price rose by $32\%$ overall across those four years.

Q8[3 marks]

Item A has a price index of $160$ and item B has a price index of $100$ , both for 2023 based on 2020. Item B is given a weight of $3$ .

If the composite index of the two items is $130$ , find the weight of item A.

Show worked solution

Let the weight of item A be $w$ . Write the composite index formula and substitute everything that is known:

\frac{w(160)+3(100)}{w+3}=130

Clear the denominator and collect the terms in $w$ on one side:

160w+300=130w+390 \Rightarrow 30w=90 \Rightarrow w=3

Answer

The weight of item A is $3$ . Check: $\frac{3(160)+3(100)}{3+3}=\frac{780}{6}=130$ , which matches the given composite index.

These four look like different questions, yet each is the same relationship rearranged: an index, a base-year price, and a later price, any two of which give the third. Once you fix the base year first and substitute carefully, Index Numbers becomes one of the most dependable sources of marks in the paper.

Key method points

These four examples rehearse the everyday moves behind almost every Index Numbers question in Add Math. Keep the following points in mind as you practise more.

A price index is $\frac{P_1}{P_0}\times 100$ : the price at the time of interest over the base-year price, times one hundred.
An index of $100$ means no change; above $100$ is a rise and below $100$ is a fall, and the amount away from $100$ is the percentage change.
To find a later price, rearrange to $P_1=\frac{I}{100}\times P_0$ ; to recover a base-year price, rearrange to $P_0=\frac{P_1\times 100}{I}$ .
A rise of $k\%$ gives the index $100+k$ ; a fall of $k\%$ gives $100-k$ .
Always check by substituting your answer back into $\frac{P_1}{P_0}\times 100$ to confirm it returns the given index.
Because marking is analytic, a clear formula-and-substitution line still earns method marks even if the final arithmetic slips.

How a teacher helps

When a student drops a mark here, it is nearly always a mix-up over which price is the base, the one that belongs on the bottom of the fraction, or a percentage read the wrong way. In a one-to-one lesson our teacher watches the exact line where that happens and fixes the habit before it settles into a routine.

Because our teachers are experienced, you work with someone who explains why the base-year price sits on the denominator, not only how to plug numbers in. Lessons are taught in English, while SPM papers are set in both Malay and English, so the notation reads the same to you in either version.

Get 1-to-1 help.

Book a Trial Class

Frequently asked questions

What exactly does a price index of 125 mean?

It means the price is $125\%$ of its base-year value, a rise of $25\%$ . An index equal to $100$ means the price is unchanged from the base year, and an index below $100$ means it has fallen.

Which price goes on the bottom of the fraction?

The base-year price $P_0$ is the denominator, and the price you are comparing, $P_1$ , is the numerator: $I=\frac{P_1}{P_0}\times 100$ . Swapping the two is the most common slip.

How do I turn a percentage change into an index?

Add to or subtract from $100$ . A rise of $20\%$ gives $120$ ; a fall of $8\%$ gives $92$ .

Then scale a price with $P_1=\frac{I}{100}\times P_0$ .

Do I need a calculator for these?

In the SPM you may use a non-programmable scientific calculator, but these easy examples use small numbers you can handle by hand, which makes checking each line of working faster.

Source:SRC-DSKP-EN

Written by the spmaddmath.com.my editorial team.· Last updated 5 September 2026

Index Numbers, Worked Examples (easy)

What these examples cover

Worked examples

Key method points

How a teacher helps

Frequently asked questions

Ready to get started?