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Line Graph Solved Questions

A line graph plots values over time (or another ordered variable) as points joined by straight segments — each point’s height is read off the same way a bar’s height is, and once you’ve read the numbers correctly it’s the same percentage, average and ratio work as any other Data Interpretation format. This page covers that core idea, multi-line graphs comparing two series, and why you shouldn't extrapolate a trend beyond the plotted points, with several fully worked examples.

Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-05. Editorial standards & corrections

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The concept, quickly

  • Each point on the line represents a value at that year (or period) on the scale shown on the axis — read it against the axis markings, not by guessing from the slope.
  • A percentage change between two points uses the same rule as any other percentage question: (new − old) / old × 100, with the EARLIER point as the original value.
  • A steep rising segment means a big increase and a steep falling segment means a big decrease — but "steep" is only a rough guide; for "which period had the largest change" questions, calculate every segment’s change first rather than eyeballing the slope.
  • An average across several points is just their sum divided by the count, exactly like a bar graph or table — the format doesn’t change the formula, only how you read the input values.
  • Some line graphs plot TWO or more lines on the same axes (e.g. the sales of two different companies over the same years) — read each line separately against the shared scale. A "when did A overtake B" question just means finding the first plotted point where A's value exceeds B's.
  • Never extrapolate a trend beyond the plotted points. A line graph only tells you what happened at the years actually shown — projecting the slope forward into an unshown year assumes the pattern continues exactly, which the chart itself does not confirm.

Worked examples

1. A line graph shows the number of candidates (in thousands) who registered for an exam over five years: 2020 – 200, 2021 – 250, 2022 – 300, 2023 – 270, 2024 – 360. Find the percentage increase in registrations from 2020 to 2021.

Solution

  1. Increase = 250 − 200 = 50.
  2. Percentage increase = (50/200) × 100 = 25%.

Answer: 25%

2. Using the same data (2020 – 200, 2021 – 250, 2022 – 300, 2023 – 270, 2024 – 360), find the average number of candidates (in thousands) registered per year over the five years.

Solution

  1. Sum = 200 + 250 + 300 + 270 + 360 = 1380.
  2. Average = 1380 / 5 = 276.

Answer: 276 thousand

3. Using the same data, find the ratio of registrations in 2022 to registrations in 2024.

Solution

  1. Ratio = 300 : 360.
  2. Dividing both terms by their HCF, 60: 5 : 6.

Answer: 5 : 6

4. Using the same data, which year-to-year segment had the largest percentage change in either direction, and what was it?

Solution

  1. Check every segment: 2020→2021: +50, (50/200)×100 = 25%. 2021→2022: +50, (50/250)×100 = 20%. 2022→2023: −30, (30/300)×100 = 10% decrease. 2023→2024: +90, (90/270)×100 ≈ 33.3%.
  2. The largest change in magnitude is 2023→2024, at approximately 33.3%.

Answer: 2023 to 2024, about a 33.3% increase

5. A line graph shows annual profit (₹ lakh) of two companies: 2020: P=40, Q=55; 2021: P=60, Q=50; 2022: P=70, Q=65. In which year did Company P's profit first exceed Company Q's?

Solution

  1. In 2020, P (40) < Q (55). In 2021, P (60) > Q (50) for the first time.
  2. So 2021 is the first year P overtakes Q (and it stays ahead in 2022 as well: 70 > 65).

Answer: 2021

6. Using the same data, find the total combined profit of both companies in 2022.

Solution

  1. Total = P + Q in 2022 = 70 + 65 = ₹135 lakh.

Answer: ₹135 lakh

7. A line graph shows a company's sales rising from 100 (2020) to 130 (2021) to 160 (2022). Someone claims that in 2023, sales will "obviously" be 190. Is this a safe conclusion to draw directly from the graph?

Solution

  1. The graph only shows data through 2022, where the year-on-year increase happened to be a constant 30 units each time (100→130→160).
  2. Claiming 2023 will be 190 assumes that this exact 30-unit increase continues — but the graph itself provides no data point confirming that, and real-world trends can change due to factors the chart doesn't capture.
  3. So this is an assumption based on an observed pattern, not something the graph actually shows.

Answer: No — it assumes the trend continues unchanged, which the graph does not confirm

Try these yourself

Read the plotted values carefully, then check against the answer.

1. Using the same data (2020 – 200, 2021 – 250, 2022 – 300, 2023 – 270, 2024 – 360 thousand), find the percentage change in registrations from 2022 to 2023.

Answer: 10% decrease

2. Using the same data, find the total registrations (in thousands) across 2020, 2021 and 2022 combined.

Answer: 750 thousand

3. Using the same data, find the ratio of registrations in 2021 to registrations in 2024.

Answer: 25 : 36

4. A line graph shows revenue (₹ lakh) of two stores: 2020: A=35, B=50; 2021: A=55, B=48; 2022: A=65, B=60. In which year did Store A's revenue first exceed Store B's?

Answer: 2021. A (55) > B (48) for the first time; A was behind in 2020.

5. Using the same data, find the total combined revenue of both stores in 2021.

Answer: ₹103 lakh. 55 + 48.

6. A line graph shows a town's population rising from 10,000 (2018) to 12,000 (2019) to 14,500 (2020). Is it safe to assume the 2021 population will be exactly 17,000, based only on this graph?

Answer: No. The year-on-year increases (2,000, then 2,500) aren't even constant, so extending the pattern to exactly 17,000 is an unsupported assumption, not something the graph confirms.

7. Using the town population data (2018: 10,000; 2019: 12,000; 2020: 14,500), find the average population over the three years.

Answer: ≈ 12,166.67. (10,000+12,000+14,500)/3.

All 14 practice questions on Line Graph, with answers →

Where this comes up

Line Graph is tested directly in the Quantitative/Numerical Aptitude section of exams Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — as a standard Data Interpretation format alongside bar graphs, pie charts and tables.

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