Quantitative Aptitude · Index Numbers

Base Shifting, Splicing and Deflating Index Numbers

Updated 1 October 2026 · Fact-checked

Base shifting changes an index series so a new year equals 100: divide every index by the new base year's old index and multiply by 100. Splicing joins two series with different bases using a common overlap year. Deflating divides a nominal value by the price index and multiplies by 100 to get the real value.

Understand Base Shifting, Splicing and Deflating

An index number compares a value in one year with the same value in a base year. The base year is always 100. An index of 125 means prices are 25% higher than in the base year.

Sometimes the base year becomes outdated. You may want to compare with a more recent year. Base shifting moves the 100 to a new year. Every index in the series is rescaled by the same factor, so the ratios between years do not change. Only the reference point changes.

Sometimes an index series is discontinued and a new series starts with a new base. Splicing joins the two into one continuous series. You need a year that appears in both series. That overlap year gives you the conversion factor. You can convert the old series to the new base, or the new series to the old base.

Deflating is different. Money values like wages or sales are nominal: they ignore price changes. To find what they are worth in base-year rupees, you divide by the price index. The result is the real value. Real wage tells you if a worker can really buy more or less than before.

Key formulas to remember

Base shifting: New index = (Old index ÷ Old index of the new base year) × 100; Apply to every year. The new base year will come out as 100, which is a quick check.
Splicing: old series to new base: Old index on new base = Old index × 100 ÷ (Old index of overlap year); The overlap year is the new series' base year, where the new series shows 100. The old series gets converted so that year becomes 100.
Splicing: new series to old base: New index on old base = New index × (Old index of overlap year) ÷ 100; Use when you want one long series that keeps the old base year as 100.
Deflating (real value): Real value = (Nominal value ÷ Price index) × 100; Use the price index (such as CPI) of the same year as the nominal value.
Real wage: Real wage = (Money wage ÷ CPI) × 100; Compare real wages across years. Do not compare money wages.
Purchasing power of money: Purchasing power of ₹1 = 100 ÷ Price index; If the index is 125, ₹1 buys 0.80 of what it bought in the base year.

How to solve Base Shifting, Splicing and Deflating questions

Identify which of the three tasks the question asks for. Then follow the steps below.

1Read the question and decide: change of base, joining two series, or converting money values to real values.
2Note the base years and the indices given. Mark the year that appears in both series (for splicing) or the new base year (for base shifting).
3Find the conversion factor. For base shifting, it is 100 ÷ old index of the new base year. For splicing, it is 100 ÷ overlap-year old index (or its reverse). For deflating, it is 100 ÷ price index.
4Multiply each required value by the factor. Do not change the overlap or base year's own value by hand. Let the formula do it.
5Check that the new base year shows exactly 100. For splicing, check that the overlap year matches in both series.
6Round only at the end, and match the answer to the option format given.

Quickest way: Factor method with option elimination

When to use it: Use in every MCQ on this topic. Calculation is only one or two divisions, so speed comes from sensible estimates.

Write the factor first: 100 ÷ (old index of new base) for shifting, or 100 ÷ price index for deflating.
Estimate the answer's direction. If the new base year's old index is above the given index, the shifted value must be below 100. If a price index is above 100, the real value must be below the nominal value.
Use this to cross out options. Real value above nominal when CPI is above 100 is always wrong.
Then compute the exact value once and pick the option.
Skip only if the question mixes several steps and you are short of time. A single-step question should take under a minute.

Common mistakes in Base Shifting, Splicing and Deflating

Dividing by the given year's index instead of the new base year's index when shifting the base.
Students confuse which year becomes 100.
Fix: The divisor is always the old index of the year that is becoming the new base. Check that this year gives 100.
Multiplying nominal value by the index when deflating.
Students remember 'index' and 'multiply by 100' but not the division.
Fix: Real value = nominal ÷ index × 100. If prices rose, the real value must be smaller than the nominal value.
Using the wrong direction in splicing, multiplying where you should divide.
There are two directions and both look alike.
Fix: Converting the old series to the new base means dividing by the overlap-year old index and multiplying by 100. Converting the new series to the old base means multiplying by the overlap-year old index and dividing by 100.
Comparing money wages across years to say a worker is better off.
Students forget prices changed too.
Fix: Always deflate first, then compare real wages.
Using the index of the wrong year when deflating.
A table with several years is read carelessly.
Fix: Match the nominal value's year with the CPI of that same year before calculating.
Treating the percentage change in index as the percentage change in real value.
Both are percentages, so they get mixed up.
Fix: Compute the real value first. Then find the percentage change in real value from those figures.

Worked examples

Example 1

An old index series with base 2018 = 100 shows: 2019 = 110, 2020 = 125, 2021 = 150, 2022 = 160. If the base is shifted to 2020, what is the index for 2022?
(A) 120
(B) 125
(C) 128
(D) 135

Show the solution

The new base year is 2020. Its old index is 125.
New index for 2022 = (160 ÷ 125) × 100.
160 ÷ 125 = 1.28, so the result is 128.
Check: 2020 gives (125 ÷ 125) × 100 = 100, as it should. 2022 is above the new base year, so a value above 100 makes sense.

Answer: (C) 128

Example 2

An old price index series has base 2015 = 100 and shows 180 for 2020. A new series starts with base 2020 = 100 and shows 115 for 2022. Using 2020 as the overlap year, what is the 2022 index on the 2015 base?
(A) 195
(B) 207
(C) 215
(D) 230

Show the solution

The overlap year is 2020. The old series gives 180 and the new series gives 100.
To put the new series on the old base, multiply by 180 ÷ 100.
2022 index on 2015 base = 115 × 180 ÷ 100.
115 × 180 = 20,700. Dividing by 100 gives 207.
Check: 2022 prices are 15% above 2020. 180 × 1.15 = 207.

Answer: (B) 207

Example 3

A worker's monthly money wage is ₹36,000 in a year when the consumer price index is 160 (base year = 100). What is the real wage?
(A) ₹20,000
(B) ₹22,500
(C) ₹25,000
(D) ₹57,600

Show the solution

Real wage = (Money wage ÷ CPI) × 100.
36,000 ÷ 160 = 225.
225 × 100 = 22,500.
Check: CPI is above 100, so the real wage must be below ₹36,000. Option D is above it, so it is out.

Answer: (B) ₹22,500

Exam tips

Questions are usually one-step. Memorise the three formulas and you can answer most within a minute.
Always check which year becomes 100. This catches most wrong options.
For deflating, estimate the direction first. If the index is above 100, the real value is lower than the nominal value.
Read splicing questions slowly. Identify the overlap year and the direction asked before you multiply.
With 0.25 negative marking, attempt a question if you can eliminate two options. A direct formula question is worth always attempting.

Practice questions from Index Numbers

Base Shifting, Splicing and Deflating: frequently asked questions

How do I shift the base of an index number?

Divide every index in the series by the old index of the year you want as the new base. Then multiply by 100. The new base year will show 100.

What is splicing of index numbers?

Splicing joins an old index series and a new one with a different base into one continuous series. You use a year present in both series to find the conversion factor. You can express the final series on either base.

What is the formula for real wages?

Real wage = (Money wage ÷ Consumer Price Index) × 100. It shows what the wage can buy in terms of base-year prices. Use the CPI of the same year as the wage.

Does base shifting change the percentage change between two years?

No. Every index is multiplied by the same factor, so the ratio between any two years stays the same. Only the reference year changes.

What is the difference between deflating and base shifting?

Base shifting rescales an index series to a new base year. Deflating uses a price index to convert money values like wages or sales into real values. They both use a ratio times 100 but serve different purposes.