A user types a long piece of content on 20 sheets, where each sheet has 55 lines and each line can contain up to 66 characters. The same content is then retyped on a new set of sheets, where each sheet has 65 lines and each line can take 70 characters. By reformatting the content in this way, what is the reduction in the number of sheets required and the corresponding percentage reduction in sheets?

Introduction / Context:
This problem deals with capacity and percentage reduction. It asks you to compare how many sheets are required to hold the same amount of text when the number of lines per sheet and characters per line change. This type of question tests multiplication, division, and percentage calculation skills in a practical formatting context.

Given Data / Assumptions:

• Original typing format: 20 sheets, 55 lines per sheet, 66 characters per line.
• New typing format: 65 lines per sheet, 70 characters per line.
• The total amount of content (characters) remains exactly the same in both formats.
• Every line is treated as fully filled for capacity calculations.

Concept / Approach:
The total text capacity can be measured in characters. First find the total number of characters in the original arrangement. Then find how many characters one new sheet can hold. Dividing the total character count by the capacity of one new sheet gives the number of new sheets needed. Finally, compare old and new numbers of sheets to get the reduction and the percentage decrease.

Step-by-Step Solution:
Step 1: Original total characters = 20 * 55 * 66. Step 2: Compute 55 * 66 = 3,630, so total characters = 20 * 3,630 = 72,600. Step 3: Capacity of one new sheet = 65 * 70 = 4,550 characters. Step 4: Number of new sheets required = 72,600 / 4,550 ≈ 15.95, so 16 sheets are needed. Step 5: Original sheets = 20, new sheets = 16, so reduction = 20 − 16 = 4 sheets. Step 6: Percentage reduction = (4 / 20) * 100% = 20%.

Verification / Alternative check:
We can also approximate by observing that the capacity per sheet increases from 55 * 66 = 3,630 characters to 4,550 characters. This is clearly more, so fewer sheets are needed. The exact calculations above confirm that only 16 sheets are required and that the reduction of 4 sheets corresponds to a 20 percent decrease, matching the computed fraction 4 / 20.

Why Other Options Are Wrong:

• 2 sheets or 10% reduction underestimates the actual saving; the math shows a bigger reduction.
• 6 sheets or 30% reduction would require only 14 sheets in the new format, which does not fit the total characters correctly.
• 8 sheets or 40% reduction would mean using only 12 sheets, which again contradicts the necessary capacity for 72,600 characters.

Common Pitfalls:
Common mistakes include rounding the intermediate values too early or confusing lines and characters. Some learners also try to compare only lines per sheet without considering characters per line. Always work with total characters to avoid miscounts and use proper rounding when computing the final number of sheets.

Final Answer:
The reduction is 4 sheets or 20% reduction.