Find the number of envelopes that can be made out of a sheet of paper 384 cm by 168 cm, if each envelope requires a piece of paper of size 16 cm by 12 cm.

Options

A. 340
B. 344
C. 336
D. 342

Answer

To find the number of envelopes that can be made from a sheet of paper measuring 384 cm by 168 cm, where each envelope requires a piece of paper sized 16 cm by 12 cm, we can follow these steps:

### Step 1: Calculate the Area of the Sheet of Paper
The area of the sheet of paper can be calculated using the formula for the area of a rectangle:

\[ \text{Area of the sheet} = \text{Length} \times \text{Breadth} \]

Substituting the values:

\[ \text{Area of the sheet} = 384 \, \text{cm} \times 168 \, \text{cm} \]

Calculating this gives:

\[ \text{Area of the sheet} = 64512 \, \text{cm}^2 \]

### Step 2: Calculate the Area of One Envelope
Next, we calculate the area required for one envelope using the same formula:

\[ \text{Area of one envelope} = \text{Length} \times \text{Breadth} \]

Substituting the values for the envelope:

\[ \text{Area of one envelope} = 16 \, \text{cm} \times 12 \, \text{cm} \]

Calculating this gives:

\[ \text{Area of one envelope} = 192 \, \text{cm}^2 \]

### Step 3: Calculate the Number of Envelopes
Now, we can find the number of envelopes that can be made by dividing the area of the sheet by the area of one envelope:

\[ \text{Number of envelopes} = \frac{\text{Area of the sheet}}{\text{Area of one envelope}} \]

Substituting the areas we calculated:

\[ \text{Number of envelopes} = \frac{64512 \, \text{cm}^2}{192 \, \text{cm}^2} \]

Calculating this gives:

\[ \text{Number of envelopes} = 336 \]

### Final Answer
Thus, the number of envelopes that can be made from the sheet of paper is **336**.

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