Quantitative Aptitude

Line Graph: Practice Questions with Answers

14 practice questions on Line Graph, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   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?

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   Answer: 2021

   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).

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2. Q.2

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

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   Answer: ₹135 lakh

   Solution:

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

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3. Q.3

   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.

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   Answer: 25%

   Solution:

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

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4. Q.4

   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?

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

   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.

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5. Q.5

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

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   Answer: 5 : 6

   Solution:

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

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6. Q.6

   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.

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   Answer: 276 thousand

   Solution:

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

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7. Q.7

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

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   Answer: 2023 to 2024, about a 33.3% increase

   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%.

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8. Q.8

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

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   Answer: 25 : 36

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9. Q.9

   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?

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   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.

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10. Q.10

    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.

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    Answer: 10% decrease

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11. Q.11

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

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

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12. Q.12

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

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    Answer: 750 thousand

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13. Q.13

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

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    Answer: ₹103 lakh. 55 + 48.

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14. Q.14

    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?

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

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