Profits earned by two companies X and Y, which produce similar kind of products, over a period of six years from 2019 to 2024 are shown in the following graph.
Question: 1
In which year did both Company X and Company Y earn the same amount of profit?
For graph and table questions, always verify values directly from the data before relying on the answer choices. Occasionally option sets may contain printing errors.
Concept:
To determine the year in which two companies earned equal profits, compare the profit values year by year.
Step 1: Compare profits for each year.
For 2019:
\[
X=6,\quad Y=9.
\]
Not equal.
For 2020:
\[
X=11,\quad Y=8.
\]
Not equal.
For 2021:
\[
X=8,\quad Y=9.
\]
Not equal.
For 2022:
\[
X=9,\quad Y=6.
\]
Not equal.
For 2023:
\[
X=8,\quad Y=8.
\]
Equal.
For 2024:
\[
X=11,\quad Y=10.
\]
Not equal.
Step 2: Identify the year.
The only year in which both companies earned identical profits is
\[
2023.
\]
Step 3: Observation regarding options.
The correct answer obtained from the data is
\[
\boxed{2023}.
\]
However, this year does not appear among the provided options, indicating an error in the question or option set.
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Question: 2
In all the years put together, what is the ratio of the yearly average profits of Company X and Company Y?
Concept:
Average profit is calculated as
\[
\text{Average Profit}
=
\frac{\text{Total Profit}}{\text{Number of Years}}.
\]
Since both companies have data for six years, we first find the total profits and then calculate their averages.
Step 1: Calculate the total profit of Company X.
\[
6+11+8+9+8+11
\]
\[
=17+8+9+8+11
\]
\[
=25+9+8+11
\]
\[
=34+8+11
\]
\[
=42+11
\]
\[
=53
\]
Therefore,
\[
\text{Total Profit of X}=53.
\]
Step 2: Calculate the total profit of Company Y.
\[
9+8+9+6+8+10
\]
\[
=17+9+6+8+10
\]
\[
=26+6+8+10
\]
\[
=32+8+10
\]
\[
=40+10
\]
\[
=50.
\]
Thus,
\[
\text{Total Profit of Y}=50.
\]
Step 3: Calculate yearly averages.
For Company X:
\[
\frac{53}{6}
=
8\frac{5}{6}.
\]
For Company Y:
\[
\frac{50}{6}
=
8\frac{1}{3}.
\]
Step 4: Form the ratio.
\[
8\frac{5}{6}:8\frac{1}{3}.
\]
Hence the required ratio is
\[
\boxed{8\frac{5}{6}:8\frac{1}{3}}.
\]
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Question: 3
What is the percentage increase in the profit of Company X from 2019 to 2024?
Show Hint
Always use the original year's value as the denominator when calculating percentage increase.
Concept:
Percentage increase is calculated using
\[
\text{Percentage Increase}
=
\frac{\text{Increase}}{\text{Original Value}}
\times 100.
\]
Step 1: Identify the profits.
Profit in 2019:
\[
6.
\]
Profit in 2024:
\[
11.
\]
Step 2: Calculate the increase.
\[
11-6=5.
\]
Thus profit increased by
\[
5 \text{ crores}.
\]
Step 3: Apply percentage increase formula.
\[
\frac{5}{6}\times100
=
83\frac{1}{3}\%.
\]
Thus mathematically the percentage increase is
\[
\boxed{83\frac{1}{3}\%}.
\]
Observation:
This value does not match any of the given options. Therefore there appears to be an error in either the graph values or the option set supplied in the question paper.
