Study the following bar-graph carefully and answer the following question. The bar-graph shows the number of pens (in thousand) sold by three shopkeepers X, Y and Z in 5 different years. The total number of pens sold by shopkeeper X in years 2020 and 2022 taken together is what percentage less than the total number of pens sold by shopkeeper Z in years 2021 and 2024 taken together? (correct to two decimal places)
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When a data interpretation question gives a result that seems impossible (e.g., asking "how much is A less than B" when A \textgreater B), double-check your reading of the graph and the question. If the numbers are correct, the question itself may be flawed.
Step 1: Read the required data from the bar graph.
- Pens sold by X in 2020 = 90 (thousand)
- Pens sold by X in 2022 = 70 (thousand)
- Pens sold by Z in 2021 = 50 (thousand)
- Pens sold by Z in 2024 = 40 (thousand) - It seems the bar is 20, let's re-read. Z in 2024 is 20.
Step 2: Calculate the total sales for each group.
- Total for X (2020 & 2022) = \(90 + 70 = 160\) thousand.
- Total for Z (2021 & 2024) = \(50 + 20 = 70\) thousand.
Let me re-read the question. "what percentage less than". This implies the second value is the base.
Let's re-read the graph values.
X in 2020: 90. X in 2022: 70. Total = 160.
Z in 2021: 50. Z in 2024: 20. Total = 70.
The question seems inconsistent. "160 is what percentage less than 70?" doesn't make sense as 160 is greater. There must be a misinterpretation of the question or graph. Let's assume the question meant Z's sales are the first value and X's are the base.
Let's re-calculate.
Total pens by Z in 2021 and 2024 = 50 + 20 = 70.
Total pens by X in 2020 and 2022 = 90 + 70 = 160.
Let's assume the question is: (Total pens by Z) is what percentage less than (Total pens by X).
Percentage Less = \( \frac{160 - 70}{160} \times 100 = \frac{90}{160} \times 100 = 56.25% \). Not an option.
Let's re-read the graph. X is blue, Y is orange, Z is grey.
X in 2020: 90. X in 2022: 70. Total X = 160.
Z in 2021: 50. Z in 2024: 20. Total Z = 70.
The question must have a typo. Let's assume it's asking for (Total pens by Y) instead of X.
Y in 2020: 40. Y in 2022: 20. Total Y = 60.
Is 60 what percentage less than 70 (Z's total)? \( \frac{70-60}{70} \times 100 = 14.28% \). No.
Let's assume the question meant something else.
Let's assume the values for Z are from 2020 and 2022. Z in 2020 = 60, Z in 2022= 30. Total = 90.
Is 90 what percent less than 160 (X's total)? \( \frac{160-90}{160} \times 100 = 43.75% \). No.
Let's try the calculation as written one more time. The question could be flawed.
Total X = 160. Total Z = 70. It asks how much X is less than Z. This is impossible.
Let's swap the roles: How much is Z less than X?
Percentage Less = \( \frac{160 - 70}{160} \times 100 = 56.25% \).
There must be a typo in the question's text. Let's find a combination that gives 11.11%. 11.11% is 1/9. This means (Base - Value) / Base = 1/9. So Value = (8/9) Base.
Let's assume the base is X's total = 160. Value = (8/9)160 = 142.22. Not likely.
Let's assume the value is X's total = 160. Base = 160 (9/8) = 180.
Is there a combination for Z that equals 180? No.
Let's assume Z's total (70) is the value. Base = 70 (9/8) = 78.75.
Let's assume Z's total (70) is the base. Value = (8/9)70 = 62.22.
There seems to be a clear error in the question text.
