Line Charts
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Solved Examples
Study MaterialSolved Examples – Line Charts
Solved examples help students understand the practical application of line charts, trend analysis, percentages, averages, and comparative analysis in Data Interpretation questions. These examples are designed from basic to advanced level and cover important questions frequently asked in SSC, Banking, Railway, Insurance, CAT, CDS, NDA, MBA entrance exams, and various competitive examinations.
Topics Covered in Solved Examples
- Trend Analysis
- Average Problems
- Percentage Increase and Decrease
- Comparative Analysis
- Profit Percentage
- Approximation Techniques
- Highest and Lowest Value Problems
- Growth Analysis
Study the Following Data Carefully
The following table represents the sales (in lakhs) of a company during six years.
| Year | Sales (₹ Lakhs) |
|---|---|
| 2018 | 120 |
| 2019 | 140 |
| 2020 | 160 |
| 2021 | 150 |
| 2022 | 180 |
| 2023 | 210 |
In a line graph, these values are plotted and connected using straight lines.
Example 1: Highest Sales Problem
Question: In which year were the sales maximum?
Solution:
Compare all sales values:
- 2018 → 120
- 2019 → 140
- 2020 → 160
- 2021 → 150
- 2022 → 180
- 2023 → 210
Highest value = 210
Answer: 2023
Example 2: Lowest Sales Problem
Question: In which year were the sales minimum?
Solution:
Lowest sales value = 120
Answer: 2018
Example 3: Total Sales Calculation
Question: Find the total sales during all six years.
Solution:
Total Sales
= 120 + 140 + 160 + 150 + 180 + 210
= 960 lakhs
Answer: ₹960 lakhs
Example 4: Average Sales Problem
Question: Find the average sales during the six years.
Solution:
Average
= Total Sales / Number of Years
= 960 / 6
= 160 lakhs
Answer: ₹160 lakhs
Example 5: Percentage Increase Problem
Question: Find the percentage increase in sales from 2018 to 2019.
Solution:
Old Value = 120
New Value = 140
Increase
= 140 − 120
= 20
Percentage Increase
= (20 / 120) × 100
= 16.67%
Answer: 16.67%
Example 6: Percentage Decrease Problem
Question: Find the percentage decrease in sales from 2020 to 2021.
Solution:
Old Value = 160
New Value = 150
Decrease
= 160 − 150
= 10
Percentage Decrease
= (10 / 160) × 100
= 6.25%
Answer: 6.25%
Example 7: Difference Between Two Years
Question: Find the difference in sales between 2023 and 2018.
Solution:
2023 Sales = 210
2018 Sales = 120
Difference
= 210 − 120
= 90 lakhs
Answer: ₹90 lakhs
Example 8: Consecutive Year Growth Problem
Question: During which period was the highest increase in sales observed?
Solution:
Increase values:
- 2018 → 2019 = +20
- 2019 → 2020 = +20
- 2020 → 2021 = −10
- 2021 → 2022 = +30
- 2022 → 2023 = +30
Highest increase = 30 lakhs
Answer: 2021–2022 and 2022–2023
Example 9: Ratio Problem
Question: Find the ratio of sales in 2019 to 2023.
Solution:
2019 Sales = 140
2023 Sales = 210
Required Ratio
= 140 : 210
= 2 : 3
Answer: 2 : 3
Example 10: Approximation Problem
Question: Approximately find the average annual sales.
Solution:
Approximate Total
≈ 120 + 140 + 160 + 150 + 180 + 210
≈ 960
Average
≈ 960 / 6
≈ 160
Answer: Approximately ₹160 lakhs
Example 11: Comparison Problem
Question: Compare the combined sales of 2018 and 2019 with the sales of 2023.
Solution:
2018 + 2019
= 120 + 140
= 260
2023 Sales = 210
Difference
= 260 − 210
= 50 lakhs
Answer: Combined sales exceed by ₹50 lakhs
Example 12: Growth Percentage Problem
Question: Find the percentage growth in sales from 2018 to 2023.
Solution:
Old Value = 120
New Value = 210
Increase
= 210 − 120
= 90
Percentage Growth
= (90 / 120) × 100
= 75%
Answer: 75%
Example 13: Median Sales Problem
Question: Find the median sales value.
Solution:
Sales values:
120, 140, 150, 160, 180, 210
Middle values:
150 and 160
Median
= (150 + 160) / 2
= 155
Answer: ₹155 lakhs
Example 14: Maximum Fluctuation Problem
Question: Between which consecutive years was the maximum fluctuation observed?
Solution:
Differences:
- 20
- 20
- 10
- 30
- 30
Maximum fluctuation = 30
Answer: 2021–2022 and 2022–2023
Example 15: Fast Mental Calculation Problem
Question: Approximately what fraction of total sales was contributed by 2023?
Solution:
2023 Sales = 210
Total Sales = 960
210/960 ≈ 1/5
Answer: Approximately 1/5
Important Exam Tips
- Always read chart title and labels carefully.
- Use approximation techniques smartly.
- Improve speed in percentage calculations.
- Analyze trends systematically.
- Avoid unnecessary lengthy calculations.
- Practice mental arithmetic regularly.
- Practice previous year Data Interpretation questions.
Common Mistakes to Avoid
- Ignoring units and scale.
- Reading wrong graph points.
- Calculation mistakes in percentages.
- Ignoring trend direction.
- Assuming unavailable data.
Practicing solved examples regularly improves analytical thinking, calculation speed, and accuracy in solving Line Chart Data Interpretation questions in competitive examinations.