To solve this problem, we need to calculate the total number of pixels for the certificate when scanned at both 600 dpi and 300 dpi, then determine the percentage reduction.

First, let's calculate the total number of pixels at 600 dpi. The dimensions of the certificate are 10 inches by 10 inches, and dpi (dots per inch) indicates how many pixels fit into one inch.

The total number of pixels along one side at 600 dpi is:

$$ 10 \times 600 = 6000 \text{ pixels} $$

Since the certificate is square, its total pixel area at 600 dpi is:

$$ 6000 \times 6000 = 36,000,000 \text{ pixels} $$

Next, let's calculate the total number of pixels at 300 dpi:

The total number of pixels along one side at 300 dpi is:

$$ 10 \times 300 = 3000 \text{ pixels} $$

The total pixel area at 300 dpi is:

$$ 3000 \times 3000 = 9,000,000 \text{ pixels} $$

To find the percentage reduction in the number of pixels, we use the following formula:

$$ \text{Percentage Reduction} = \left( \frac{\text{Pixels at 600 dpi} - \text{Pixels at 300 dpi}}{\text{Pixels at 600 dpi}} \right) \times 100 $$

Substituting the values we found:

$$ \text{Percentage Reduction} = \left( \frac{36,000,000 - 9,000,000}{36,000,000} \right) \times 100 = \left( \frac{27,000,000}{36,000,000} \right) \times 100 = 75\% $$

Thus, the percentage reduction in the number of pixels when the certificate is scanned at 300 dpi instead of 600 dpi is 75%.

The correct option is Option C: 75.

Basics of GIS, GPS and Remote Sensing · Geomatics Engineering Or Surveying · GATE CE

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