A typist uses a sheet measuring 20 cm by 30 cm lengthwise. If a margin of 2 cm is left on each side and a 3 cm margin on top and bottom, then the percent of page used for typing is

Options

A. 40%
B. 60%
C. 64%
D. 72%

Answer

To find the percent of the page used for typing, we will follow these steps:

### Step 1: Calculate the total area of the sheet.
The dimensions of the sheet are given as 20 cm by 30 cm.

\[ \text{Total Area} = \text{Length} \times \text{Breadth} = 20 \, \text{cm} \times 30 \, \text{cm} = 600 \, \text{cm}^2 \]

### Step 2: Determine the effective dimensions for typing after accounting for the margins.
The margins are as follows:
- 2 cm on each side (left and right)
- 3 cm on the top and bottom

**Available Length:**
\[ \text{Available Length} = 20 \, \text{cm} - 2 \, \text{cm} - 2 \, \text{cm} = 16 \, \text{cm} \]

**Available Breadth:**
\[ \text{Available Breadth} = 30 \, \text{cm} - 3 \, \text{cm} - 3 \, \text{cm} = 24 \, \text{cm} \]

### Step 3: Calculate the area available for typing.
\[ \text{Available Area} = \text{Available Length} \times \text{Available Breadth} = 16 \, \text{cm} \times 24 \, \text{cm} = 384 \, \text{cm}^2 \]

### Step 4: Calculate the percentage of the page used for typing.
To find the percentage of the area used for typing, we use the formula:

\[ \text{Percentage Used} = \left( \frac{\text{Available Area}}{\text{Total Area}} \right) \times 100 \]

Substituting the values we calculated:

\[ \text{Percentage Used} = \left( \frac{384 \, \text{cm}^2}{600 \, \text{cm}^2} \right) \times 100 \]

Calculating this gives:

\[ \text{Percentage Used} = \left( 0.64 \right) \times 100 = 64\% \]

### Final Answer:
The percent of the page used for typing is **64%**.

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