A typist uses a sheet measuring 20 cm by 30 cm.\nMargins are left as follows: 2 cm on each side (left and right) and 3 cm on top and bottom.\nWhat percentage of the page area is used for typing?

Introduction:
This question tests area calculation with margins and percentage conversion. A margin reduces the usable typing region. Since margins are on both sides, we subtract twice the margin value from each dimension. After finding the usable (typing) area, we divide it by the total page area and multiply by 100 to get the percentage used. This is a straightforward problem, but it checks attention to “each side” and “top and bottom,” which are common sources of errors.

Given Data / Assumptions:

• Sheet size = 20 cm by 30 cm
• Side margins: 2 cm on left and 2 cm on right
• Top and bottom margins: 3 cm each
• Total area = 20 * 30
• Typing area = (20 - 2*2) * (30 - 2*3)

Concept / Approach:
Compute total area. Compute effective width and effective height after margins. Compute typing area. Then percentage used = (typing area / total area) * 100. This uses basic rectangle area and percent formula.

Step-by-Step Solution:
Total area = 20 * 30 = 600 sq cmEffective width = 20 - 2*2 = 20 - 4 = 16 cmEffective height = 30 - 2*3 = 30 - 6 = 24 cmTyping area = 16 * 24 = 384 sq cmPercentage used = (384 / 600) * 100384/600 = 64/100 = 0.64Percentage used = 64%

Verification / Alternative Check:
Reduce the fraction: 384/600 simplifies by dividing by 6 to 64/100. That directly equals 64%. This confirms the arithmetic without a calculator. The result also makes sense: margins reduce both dimensions noticeably, so used area should be significantly less than 100%.

Why Other Options Are Wrong:
74%, 84%, 94%: too high; would imply very small margins or incorrect subtraction (only subtracting once).70%: usually from rounding errors or using wrong effective dimensions.

Common Pitfalls:
Subtracting 2 cm only once instead of left + right.Subtracting 3 cm only once instead of top + bottom.Computing percentage on the remaining blank margin area instead of typing area.Arithmetic mistake in 16*24 or fraction conversion.

Final Answer:
64%