a typist uses a paper of size 32 cm × 20 cm. he leaves a margin of 2 cm each on all the sides .if he leaves a margin of 1 cm only on all the sides ,then what is the percentage of the increase in the area available for typing
2" margin: (32-4)(20-4) = 448
1" margin: (32-2)(20-2) = 540
so % increase is
(540-448)/448 * 100% = ____ %
To find the percentage increase in the area available for typing, we need to compare the initial area (with 2 cm margins) to the final area (with 1 cm margins).
Let's start by calculating the initial area:
Initial length = 32 cm - 2 cm (left margin) - 2 cm (right margin) = 28 cm
Initial width = 20 cm - 2 cm (top margin) - 2 cm (bottom margin) = 16 cm
Initial area = Initial length * Initial width
Now let's calculate the final area:
Final length = 32 cm - 1 cm (left margin) - 1 cm (right margin) = 30 cm
Final width = 20 cm - 1 cm (top margin) - 1 cm (bottom margin) = 18 cm
Final area = Final length * Final width
Lastly, we can find the percentage increase in the area:
Area increase = Final area - Initial area
Percentage increase = (Area increase / Initial area) * 100
Let's calculate the values:
Initial area = 28 cm * 16 cm = 448 cm²
Final area = 30 cm * 18 cm = 540 cm²
Area increase = 540 cm² - 448 cm² = 92 cm²
Percentage increase = (92 cm² / 448 cm²) * 100 = 20.54%
Therefore, the percentage increase in the area available for typing is approximately 20.54%.