How to Read and Solve Double Bar Graph Questions?

Double Bar Graph represents two related data sets for the same categories using paired bars. This page explains how to read the scale, compare values, calculate totals and differences, find ratios and solve common Data Interpretation questions with accurate formulas and examples.

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What is a Double Bar Graph?

A Double Bar Graph displays two values for each category through two adjacent bars. It is used to compare two related data sets across the same categories.

Each category has a pair of bars, usually identified by different colours, patterns or labels. Read the vertical axis using its scale, then record the value represented by each bar. If the bars show values A and B, their total is A + B, their difference is |A − B|, and their ratio is A:B.

Double Bar Graph Video Lessons

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Double and Stacked Bar Graphs

Learn to read double and stacked bar graphs, compare values across categories, and interpret how individual components contribute to total quantities.

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Double Bar Graph Formula & Tricks

Important Formulas

Total of two values
Total = A + B

Add the two bar values for the same category.

Absolute difference
Difference = |A − B|

Subtract the smaller value from the larger value.

Percentage by which A exceeds B
Percentage increase = ((A − B) ÷ B) × 100

Use B as the reference value when comparing how much A exceeds B.

Ratio of two values
Ratio = A:B

Write the two values in order and reduce the ratio by their greatest common divisor.

Average of two values
Average = (A + B) ÷ 2

Add the paired values and divide by 2.

Quick Tricks

Read the scale before reading the bars

Check the numerical difference between consecutive markings on the vertical axis. A bar halfway between 20 and 30 represents 25, not 20 or 30.

Example: If the scale increases by 10 units and a bar reaches the third marking above 10, its value is 40.
Use a comparison table for multiple questions

Write the two values beside each category before calculating totals, differences or ratios. This prevents values from the two series being interchanged.

Example: For Mathematics = 40 and Science = 30, total = 70, difference = 10 and ratio = 4:3.
Keep the reference value in percentage comparisons

For the percentage by which A is greater than B, divide the difference by B. Reversing the reference changes the result.

Example: If A = 50 and B = 40, A exceeds B by ((50 − 40) ÷ 40) × 100 = 25%.

Double Bar Graph Concepts

Reading paired bars and the scale

The value of each data set is obtained from its own bar, while both bars in a pair correspond to the same category.

First identify the category on the horizontal axis. Then identify the series using the legend and read the height of each bar from the vertical scale. Do not compare bar heights without checking that both bars use the same axis.

Example: If Class C has Mathematics bar 50 and Science bar 45, the two values for Class C are 50 and 45.

Finding totals and differences

For a category with values A and B, the combined total is A + B and the difference is |A − B|.

Use the total when the question asks for the number represented by both series together. Use the absolute difference when it asks how many more or fewer one series has than the other.

Example: For values 50 and 45, total = 95 and difference = |50 − 45| = 5.

Calculating ratios and percentage comparisons

The ratio of two bar values is written as A:B, while percentage comparison uses the specified reference value in the denominator.

For values A and B, reduce A:B to its simplest form. If A is compared with B as an increase, calculate ((A − B) ÷ B) × 100. If B is compared with A, use A as the denominator.

Example: For Mathematics = 40 and Science = 30, the ratio is 40:30 = 4:3, and Mathematics is greater by (10 ÷ 30) × 100 = 33⅓%.

Comparing totals across categories

To compare two categories across both data sets, add the paired values within each category and then compare the resulting totals.

If category X has values A₁ and B₁ and category Y has values A₂ and B₂, compare A₁ + B₁ with A₂ + B₂. This is different from comparing only one series.

Example: Class A total = 40 + 30 = 70 and Class D total = 45 + 50 = 95, so Class D has 25 more students in total.

Double Bar Graph Visual Guide & Data

Use the table and chart below to understand the data better.

Source data for the Double Bar Graph

Number of students choosing Mathematics and Science in four classes

Class Mathematics Science
Class A 40 30
Class B 35 40
Class C 50 45
Class D 45 50

Note: Each class is represented by two adjacent bars, one for Mathematics and one for Science.

Students choosing Mathematics and Science

Visual guide: Students choosing Mathematics and Science
Paired bars compare the two subjects across four classes

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Practice Double Bar Graph Questions

Practise published questions related to this topic.

1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

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Double Bar Graph Quick Quiz

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Quick Revision Notes

Double Bar Graph Revision Points

Use these rules while solving paired-bar Data Interpretation questions.

  • A double bar graph has two bars for every category.
  • Read the legend and vertical-axis scale before recording values.
  • Total for a category = first value + second value.
  • Difference = absolute difference between the two values.
  • Ratio of values A and B = A:B, reduced to simplest form.
  • Percentage by which A exceeds B = ((A − B) ÷ B) × 100.
  • To compare categories using both series, add the two bars in each category first.

Related Topic Explainers

Bar Graph Data Interpretation →

Double Bar Graph FAQs

Is there one fixed Double Bar Graph formula?

No. The graph itself has no single fixed formula. Common calculations use Total = A + B, Difference = |A − B|, Ratio = A:B and percentage comparison = ((A − B) ÷ B) × 100 when A is compared with B.

If Mathematics is 50 and Science is 40, by what percentage is Mathematics higher?

Mathematics is higher by ((50 − 40) ÷ 40) × 100 = 25%.

How do you find the ratio when two bars show 45 and 30?

The ratio is 45:30. Dividing both terms by 15 gives 3:2.

What is the combined value if the two bars for a category are 35 and 40?

Combined value = 35 + 40 = 75.

How is the average of two bars calculated?

Add the two values and divide by 2. For values 50 and 45, the average is (50 + 45) ÷ 2 = 47.5.

How do you compare two classes using both bars?

Add the two values for each class, then compare the totals. For example, Class A total is 40 + 30 = 70, while Class D total is 45 + 50 = 95; Class D is higher by 25.

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